HCF of co-prime numbers 4 and 15 was found as follows by factorisation

1. Factors and Multiples:

(i) A factor of a number is that number which divides the number exactly.

(ii) A multiple of a number is exactly divisible by the number.

(iii) Every number is a factor as well as a multiple of itself.

(iv) 1 is a factor of every number and is the only number, which has exactly one factor.

(v) Every number other than 1 has at least two factors, namely 1 and the number itself.

(vi) Every number other than 1 can be uniquely expressed as the product of prime numbers, except for the order of prime numbers.

2. Prime Number:

A number having no factor other than 1 and the number itself is called a Prime number. In other words, a Prime number has exactly two distinct factors, 1 and the number itself.

3. Composite number:

(i) A number having factors other than 1 and the number itself is called a Composite number.

(ii) The number 1 is neither a Prime nor a Composite number, because it has a single factor.

4. Even and Odd Numbers:

(i) Numbers divisible by 2 are called Even numbers.

(ii) Numbers not divisible by 2 are called Odd numbers.

(iii) 2 is the only even Prime number.

(iv) Every prime number other than 2 is odd, but every odd number is not necessarily a prime number.

(v) Every even number greater than 4 can be expressed as the sum of two odd prime numbers.

5. Twin Primes:

Primes occurring in pairs with a difference of two are called Twin primes.

6. Divisibility Test:

(i) A number is divisible by 2, if the unit’s digit of the number is 0, 2, 4, 6 or 8.

(ii) A number is divisible by 3, if the sum of the digits is divisible by 3.

(iii) A number is divisible by 4, if the number formed by its digits in ten’s and unit’s places is divisible by 4.

(iv) A number is divisible by 5, if unit’s digit is 0 or 5.

(v) A number is divisible by 6, if it is divisible by both 2 and 3.

(vi) A number is divisible by 8, if the number formed by its digits in hundred’s, ten’s and unit’s places is divisible by 8.

(vii) A number is divisible by 9, if the sum of the digits is divisible by 9.

(viii) A number is divisible by 10, if the unit’s digit is 0.

(ix) A number is divisible by 11, if the difference of the sum of its digits in odd places and the sum of its digits in even places (starting from unit’s place) is either 0 or divisible by 11.

7. HCF and LCM:

(i) The H.C.F. of two or more numbers is the largest number that divides all the given numbers.

(ii) The L.C.M. of two or more numbers is the smallest number which is divisible by all the given numbers.

8. Properties of HCF and LCM:

(i) The product of H.C.F. and L.C.M. of two numbers equals their product. This result may not be true for more than two numbers.

(ii) The H.C.F. of any two prime or co-prime numbers equals 1.

(iii) The L.C.M. of any two prime or co-prime numbers equals their product.

(iv) The H.C.F. of two or more numbers is never greater than any of the numbers.

(v) The L.C.M. of two or more numbers is never less than any of the numbers.

(vi) The H.C.F. of two or more numbers is a factor of their L.C.M.

(vii) If x is a factor of y, then the H.C.M. of x and y is x and L.C.M. of x and y is y.

Last updated at Jan. 3, 2019 by Teachoo

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Ex 3.6, 3 HCF of co-prime numbers 4 and 15 was found as follows by factorization : 4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF? HCF of 4 & 5 We do prime factorisation of both 4 and 5 Thus, 4 = 2 × 2 15 = 3 × 5 Since there are no prime common factors The only common factor will be 1 So, HCF = 1 ∴ HCF will not be 0, but 1.

Question 3 Exercise 3.5

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Answer:

SOLUTION:

no, the answer is not correct. because 0 cannot be a common factor of any number. if there is no common factor it means that 1 is the common factor.

hence, HCF of 4 and 15 is 1.

Video transcript

Welcome to leader homework today. We are looking at question number three the question is it safe to go prime numbers 4 and 15 was found as follows by factorization, but somehow they found it was that the reward for as 22 and they wrote 15 estates by right. These are the primary thing that always agreed. Right. So the smallest common factor or the smallest thing the smallest of a factor that must be that is in its EF where there is no common framework. This is one. Okay, so your answer is 1 so, thank you.

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