19. Find the greatest number which divides 72 and 84 without leaving a remainder.
Answers
Greatest Common Factor of 72 and 84 is the largest possible number which divides the numbers 72 and 84 exactly leaving the remainder as 0
GCF of 72 and 84 is 12
We can find the GCF by the following two methods.
Long division Method
Prime factorization Method
GCF of 72 and 84 by Long Division
Step 1: Divide 72 by 84 and check the remainder.
Step 2: Make the remainder of the above step as the divisor and the divisor of the above step as the dividend and perform the long division again.
Step 3: Continue till you get the remainder as 0
GCF of 72 and 84 by Long Division
GCF of 72 and 84 by Prime Factorization
We will express the numbers 72 and 84 as a product of their prime factors.
GCF of 72 and 84 by Prime Factorization
Prime factorization of 72 is 2 × 2 × 2 × 3 × 3
Prime factorization of 84 is 2 × 2 × 3 × 7
The common factors in both prime factorization = 2 × 2 × 3
GCF is the product of the prime factors that are common to the prime factorization of 72 and 84
So, GCF of 72 and 84 is 12
You can find the GCF in any of the above methods but the solution will be the same.
Answer: GCF of 72 and 84 is 12