Question

How do you find the GCF of $12$ and $56$ ?

Answer 1

Hint: In this question you are required to find the GCF or in other words, the greatest common factor of the two given numbers that are $12$ and $56$. To solve this question factorise both $12$ and $56$ and then find the common multiple between them.

Complete step by step answer:
The GCF or Greatest Common Factor of a set of whole numbers is the largest positive integer that divides all the numbers in the set evenly.
To find GCF let us first write the factors of both $12$ and $56$
Factors of $12$ are: $1,2,3,4,6$ and $12$
Factors of $56$ are: $1,2,4,7,8,14,28$ and $56$

As we can notice the factors of both the given integers we can easily tell that $4$ is the largest positive integer that divides both $12$ and $56$ evenly.
Therefore, $4$ is the Greatest Common Factor of $12$ and $56$.

Note: The GCF is also known as –
Greatest Common Denominator (GCD) or Highest Common Factor (HCF) or Greatest Common Divisor (GCD).
- There are other ways also to compute the GCF of a set of numbers depending upon how many numbers you have to calculate the GCF and how large are the values of the given integers.
- One of the other methods is by PRIME FACTORISATION METHOD. This method is applied when you are required to find the GCF of larger numbers because in that case it is difficult to list out all of the factors. Therefore to fix this one can use this prime factorisation method.
Prime Factors of $12$: $2 \times 2 \times 3$
Prime Factors of $56$: $2 \times 2 \times 2 \times 7$
After finding the prime factors in $12$ and $56$ we can notice that the common prime factors are $2 \times 2$ which is nothing but $4$.