What is the smallest number with which 200 factorial should be multiplied to make it divisible by 12 100?

Find the smallest number by which 200 should be multiplied to make it a perfect cube

Table of Contents Show

What are Factors of 100?
How to Calculate the Factors of 100?
Factors of 100 by Prime Factorization
Factors of 100 in Pairs
FAQs on Factors of 100
What are Factor Pairs of 100?
What are the Factors of 100 and 75?
What are the Negative Factors of 100?
What are Common Factors of 100 and 25?
What are the Factors of 100?

2	200
2	100
2	50
5	25
5	5
	1

We find 200 = `bar(2 xx 2 xx 2) xx 5 xx 5`

Grouping the prime factors of 200 as triplets, we are left with 5 × 5

We need one more 5 to make it a perfect cube.

So to make 200 a perfect cube multiply both sides by 5.

200 × 5 = `(bar(2 xx 2 xx 2) xx 5 xx 5) xx 5`

1000 = 2 × 2 × 2 × 5 × 5 × 5 × 5 × 5

Now 1000 is a perfect cube.

∴ The required number is 5.

Concept: Concept of Cube Root

Is there an error in this question or solution?

Factors of 100 are the collection of both positive and negative numbers which can be evenly divided into 100. The word hundred was invented in 1920 by nine-year-old Milton Sirotta (1911-1981), nephew of Edward Kasner, a U.S. mathematician. Learning about the factors of 100 is useful in learning advanced Maths concepts. In this lesson, we will calculate the factors of 100, its prime factors, its factors in pairs, and we will finish by solving some examples for better understanding.

Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, and 100
Factors of -100: -1, -2, -4, -5, -10, -20, -25, -50 and -100
Prime Factorization of 100: 100 = 22 × 52

What are Factors of 100?

The factors of 100 are all the integers 100 can be divided into. The number 100 is an even composite number.

As it is even, it will have 2 as its factor. To understand why it is composite, let's recall the definition of a composite number. A number having a total count of factors in excess of two is defined as a composite number. On the other hand, a number such as 17 is a prime number because it has only 2 factors i.e. 1 and 17.

Now accordingly the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

How to Calculate the Factors of 100?

Let's begin calculating the factors of 100, starting with the smallest whole number, i.e., 1. Divide 100 with this number. Is the remainder 0? Yes! So, we will get:

100 ÷ 1 = 100
100 × 1 = 100

The next whole number is 2. Now divide 100 with this number:

100 ÷ 2 = 50
2 × 50 = 100

Proceeding in a similar manner, we get other numbers 100 can be divided by. They can be written as:

1 × 100 = 100
2 × 50 = 100
4 × 25 = 100
5 × 20 = 100
10 × 10 = 100

Explore factors using illustrations and interactive examples:

Factors of 175 - The factors of 175 are 1, 5, 7, 25, 35, 175
Factors of 15 - The factors of 15 are 1, 3, 5, 15
Factors of 25 - The factors of 25 are 1, 5, 25
Factors of 35 - The factors of 35 are 1, 5, 7, 35
Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

Factors of 100 by Prime Factorization

Prime factorization means expressing a composite number as the product of its prime factors.

Step 1: To get the prime factorization of 100, we divide it by its smallest prime factor, 2 like 100 ÷ 2 = 50.
Step 2: Now, 50 is divided by its smallest prime factor, and the quotient is obtained.
Step 3: This process goes on till we get the quotient as 1.
The prime factorization of 100 in the form of a factor tree is shown below.

The above factorization is the tree diagram representation of factors of 100. Therefore, factors of 100 = 2 × 2 × 5 × 5

Q: Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not?

A: And as you might have already guessed, for prime numbers, there are no other factors.

Factors of 100 in Pairs

The pair, consisting of numbers that give 100 when multiplied, is known as the factor pair of 100. The following are the factors of 100 in pairs:

The product form of 100	Pair factor
1 × 100 = 100	(1, 100)
2 × 50 = 100	(2, 50)
4 × 25 = 100	(4, 25)
5 × 20 = 100	(5, 20)
10 × 10 = 100	(10, 10)
20 × 5 = 100	(20, 5)
25 × 4 = 100	(25, 4)
50 × 2 = 100	(50, 2)
100 × 1 = 100	(100, 1)

Observe in the table above, after 10 × 10, the factors start repeating. So, it is enough to find factors until (10,10). If we consider negative integers, then both the numbers in the pair factors will be negative i.e. - ve (×) - ve = + ve.

So, we can have negative factor pairs of 100 as (-1,-100), (-2,-50), (-4,-25), (-5,-20), and (-10,-10).

Important Notes:

The numbers which we multiply to get 100 are the factors of 100.
Factors of 100 are written as 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Factor pairs are the pairs of two numbers that, when multiplied, give the original number. The pair factor of 100 are (1,100), (2,50), (4,25), (5,20), and (10,10).

Example 1: Help Alastair list the factors of 100 and find the factor pairs.

Solution:

Factors of 100 are the numbers that divide 100 without any remainder. They are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Factors pairs are the pairs of two numbers that, when multiplied, give 100:

1 × 100 = 100

2 × 50 = 100

4 × 25 = 100

5 × 20 = 100

10 × 10 = 100

Hence, pairs of 100 are (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10).
Example 2: Kevin has to list the factors of 100 and factors of 200 and find the common factors between them. Can you help him do it?

Solution:

Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100 and the factors of 200 are 1, 2, 4, 5, 10, 20, 25, 40, 50, 100, and 200. We can see that 1, 2, 4, 5, 10, 20, 25, 50, and 100 are the common factors of 100 and 200.

Hence, common factors of 100 and 200 are 1, 2, 4, 5,10, 20, 25, 50, and 100.
Example 3: Alina's mother promised to give her 3 chocolate cookies if she is able to list all the factors of 100. Can you help Alina list the factors of 100?

Solution:

Factors of 100 are numbers that divide 100 exactly without any remainder.

100 ÷ 1 = 100

100 ÷ 2 = 50

100 ÷ 4 = 25

100 ÷ 5 = 20

100 ÷ 10 = 10

Hence, factors of 100 are 1, 2, 4, 5,10, 20, 25, 50, and 100.

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FAQs on Factors of 100

What are Factor Pairs of 100?

The factor pairs of 100 are (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10).

What are the Factors of 100 and 75?

The factors of 100 are 100, 50, 25, 20, 10, 5, 4, 2, and 1. Similarly, factors of 75 are 1, 3, 5, 15, 25, and 75.
Therefore, the common factors of 100 and 75 are 1, 5, and 25.

What are the Negative Factors of 100?

Negative factors of 100 are written as -1, -2, -4, -5, -10, -20, -25, -50, and -100.

What are Common Factors of 100 and 25?

Factors of 100 are written as 1, 2, 4, 5, 10, 20, 25, 50, and 100 and the factors of 25 are 1, 5, and 25.
Hence, Common factors of 100 and 25 are 1, 5, and 25.

What are the Factors of 100?

Factors of 100 are written as 1, 2, 4, 5, 10, 20, 25, 50, and 100.

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Given a number, the only operation allowed is to multiply the number by 2. Calculate the minimum number of operations to make the number divisible by 10.
NOTE: If it is not possible to convert then print -1.
Examples:

Input: 10
Output: 0 As the given number is itself divisible by 10, the answer is 0.
Input: 1

Output: -1 As by multiplying with 2, given no. can’t be converted into a number that is divisible by 10, therefore the answer is -1.

Approach: Any given number is divisible by 10 only if the last digit of the number is 0. For this problem, extract the last digit of the input number and check it in the following ways : 1) If the last digit is 0 then it is already divisible by 10 , so the minimum number of steps is 0.2) If the last digit is 5 then multiplying it by 2 one time will make it divisible by 10, so the minimum number of steps is 1.3) If the last digit is an even or odd number (apart from 0 and 5) then multiplying it by 2 any number of times will only produce even number so we can never make it divisible by 10. Therefore the number of steps is -1.

#include <bits/stdc++.h>
using namespace std;
int multiplyBy2(int n)
{
    int rem, value;
    rem = n % 10;
    switch (rem) {
    case 0:
        value = 0;
        break;
    case 5:
        value = 1;
        break;
    default:
        value = -1;
    }
    return value;
}
int main()
{
    int n = 28;
    cout << multiplyBy2(n) << endl;
    n = 255;
    cout << multiplyBy2(n) << endl;
  return 0;
}

import java.io.*;
class GFG
{
    static int multiplyBy2(int n)
{
    int rem, value;
    rem = n % 10;
    switch (rem)
    {
    case 0:
        value = 0;
        break;
    case 5:
        value = 1;
        break;
    default:



        value = -1;
    }
    return value;
}
public static void main (String[] args)
{
    int n = 28;
    System.out.println(multiplyBy2(n));
    n = 255;
    System.out.println(multiplyBy2(n));
}
}

def dig(argu):
    switcher = {
        0: 0,
        5: 1,
    }
    return switcher.get(argu, -1)
def multiplyBy2(n):
    rem = n % 10;
    return dig(rem);
n = 28;
print(multiplyBy2(n));
n = 255;
print(multiplyBy2(n));

using System;
class GFG
{
    static int multiplyBy2(int n)
    {
    int rem, value;
    rem = n % 10;
    switch (rem)
    {
    case 0:
        value = 0;
        break;
    case 5:
        value = 1;
        break;
    default:
        value = -1;
        break;
    }
    return value;
}
public static void Main ()
{
    int n = 28;
    Console.WriteLine(multiplyBy2(n));
    n = 255;
    Console.WriteLine(multiplyBy2(n));
}
}

<?php
function  multiplyBy2($n)
{
     $rem;



     $value;
    $rem = $n % 10;
    switch ($rem) {
    case 0:
        $value = 0;
        break;
    case 5:
        $value = 1;
        break;
    default:
        $value = -1;
    }
    return $value;
}
    $n = 28;
    echo  multiplyBy2($n),"\n";
    $n = 255;
        echo  multiplyBy2($n),"\n";
?>

<script>
    function multiplyBy2(n)
    {
        var rem, value;
        rem = n % 10;
        switch (rem) {
        case 0:
            value = 0;
            break;
        case 5:
            value = 1;
            break;
        default:
            value = -1;
        }
        return value;
    }
        var n = 28;
        document.write(multiplyBy2(n)+"<br/>");
        n = 255;
        document.write(multiplyBy2(n));
</script>

#include <iostream>
using namespace std;
int main() {
int n = 10;
if (n % 10 == 0)
    cout << 0;
else{
  n = n*2;
    if (n % 10 == 0)
        cout<<0;
    else
        cout<<-1;
}
    return 0;
}

import java.io.*;



class GFG {
  public static void main (String[] args) {
    int n = 10;
    if (n % 10 == 0)
      System.out.println("0");
    else{
      n = n*2;
      if (n % 10 == 0)
        System.out.println("0");
      else
        System.out.println("-1");
    }
  }
}

n = 10
if n % 10 == 0:
    print(0)
else:
    n = n*2
    if n % 10 == 0:
        print(0)
    else:
        print(-1)

using System;
public class GFG{
  static public void Main (){
    int n = 10;
    if (n % 10 == 0)
    { Console.WriteLine("0"); }
    else{
      n = n*2;
      if (n % 10 == 0)
      { Console.WriteLine("0"); }
      else
      { Console.WriteLine("-1"); }
    }
  }
}

<script>
      let n = 10;
      if (n % 10 == 0)
          document.write(0);
      else {
          n = n * 2;
          if (n % 10 == 0)
              document.write(0);
          else
              document.write(-1);
      }
  </script>