Are you on the hunt for the GCF of 16 and 49? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in! Show
Want to quickly learn or show students how to find the GCF of two or more numbers? Play this very quick and fun video now! First off, if you're in a rush, here's the answer to the question "what is the GCF of 16 and 49?": GCF of 16 and 49 = 1 What is the Greatest Common Factor?Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. It's also commonly known as:
There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are. For smaller numbers you can simply look at the factors or multiples for each number and find the greatest common multiple of them. For 16 and 49 those factors look like this:
As you can see when you list out the factors of each number, 1 is the greatest number that 16 and 49 divides into. Prime FactorsAs the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors. List out all of the prime factors for each number:
Now that we have the list of prime factors, we need to find any which are common for each number. Since there are no common prime factors between the numbers above, this means the greatest common factor is 1: GCF = 1 Find the GCF Using Euclid's AlgorithmThe final method for calculating the GCF of 16 and 49 is to use Euclid's algorithm. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators. If you want to learn more about the algorithm and perhaps try it yourself, take a look at the Wikipedia page. Hopefully you've learned a little math today and understand how to calculate the GCD of numbers. Grab a pencil and paper and give it a try for yourself. (or just use our GCD calculator - we won't tell anyone!) Cite, Link, or Reference This PageIf you found this content useful in your research, please do us a great favor and use the tool below to make sure you properly reference us wherever you use it. We really appreciate your support!
The GCF of 16 and 16 is 16. Steps to find GCF
MathStep (Works offline)  Android and iPhone/ iPad RelatedFind hcf of: 32 & 32 8 & 8 48 & 48 80 & 80 112 & 112 32 & 16 16 & 32 48 & 16 16 & 48 80 & 16 16 & 80 112 & 16 16 & 112 Enter two numbers separate by comma. To find GCF of more than two numbers, click here. The greatest common factor (GCF) is also known as greatest common divisor (GCD) or highest common factor (HCF).
GCF of 16 and 100 is the largest possible number that divides 16 and 100 exactly without any remainder. The factors of 16 and 100 are 1, 2, 4, 8, 16 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 16 and 100 - prime factorization, Euclidean algorithm, and long division. What is GCF of 16 and 100?Answer: GCF of 16 and 100 is 4. Explanation: The GCF of two non-zero integers, x(16) and y(100), is the greatest positive integer m(4) that divides both x(16) and y(100) without any remainder. Methods to Find GCF of 16 and 100The methods to find the GCF of 16 and 100 are explained below.
GCF of 16 and 100 by Listing Common Factors
There are 3 common factors of 16 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 16 and 100 is 4. GCF of 16 and 100 by Prime FactorizationPrime factorization of 16 and 100 is (2 × 2 × 2 × 2) and (2 × 2 × 5 × 5) respectively. As visible, 16 and 100 have common prime factors. Hence, the GCF of 16 and 100 is 2 × 2 = 4. GCF of 16 and 100 by Long DivisionGCF of 16 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
The corresponding divisor (4) is the GCF of 16 and 100. ☛ Also Check:
GCF of 16 and 100 Examples
Example 2: Find the greatest number that divides 16 and 100 exactly. Solution: The greatest number that divides 16 and 100 exactly is their greatest common factor, i.e. GCF of 16 and 100.
Therefore, the GCF of 16 and 100 is 4.
Example 3: Find the GCF of 16 and 100, if their LCM is 400. Solution: ∵ LCM × GCF = 16 × 100 ⇒ GCF(16, 100) = (16 × 100)/400 = 4 Therefore, the greatest common factor of 16 and 100 is 4. go to slidego to slidego to slide
The GCF of 16 and 100 is 4. To calculate the GCF of 16 and 100, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 16 and 100, i.e., 4. What are the Methods to Find GCF of 16 and 100?There are three commonly used methods to find the GCF of 16 and 100.
What is the Relation Between LCM and GCF of 16, 100?The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 16 and 100, i.e. GCF × LCM = 16 × 100. If the GCF of 100 and 16 is 4, Find its LCM.GCF(100, 16) × LCM(100, 16) = 100 × 16 Since the GCF of 100 and 16 = 4 ⇒ 4 × LCM(100, 16) = 1600 Therefore, LCM = 400 ☛ GCF Calculator How to Find the GCF of 16 and 100 by Prime Factorization?To find the GCF of 16 and 100, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 100 = 2 × 2 × 5 × 5. ⇒ Since 2, 2 are common terms in the prime factorization of 16 and 100. Hence, GCF(16, 100) = 2 × 2 = 4 ☛ What is a Prime Number? How to Find the GCF of 16 and 100 by Long Division Method?To find the GCF of 16, 100 using long division method, 100 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as GCF. |
What is the GCF of 16?
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