Question

How do you find the GCF of 120 and 68?

Answer 1

Hint: The factor is defined as a number that completely divides another number generating the final remainder of zero. The above question can be solved in 3 steps. Firstly, we find the factors of the mentioned number 120. In step2, we find the factors of the number 68. In step3, the common factors of 120 and 68 are multiplied to get the required answer.

Complete step-by-step solution:
Factors are the numbers that are multiplied with other numbers to give the original number.
Step1:
The number 120 should be written as the product of primes.
The number 120 can be written as a product of 2’s, 3 and 5.
The factors of the numbers 120 are
$\Rightarrow 120=2\times 2\times 2\times 3\times 5$
Step2:
The number 68 should be written as the product of primes.
The number 68 can be written as a product of 2’s and 17.
The factors of the 68 are
$\Rightarrow 68=2\times 2\times 17$
Step3:
Factors of a number 120
$\Rightarrow 120=2\times 2\times 2\times 3\times 5$
Factors of a number 68
$\Rightarrow 68=2\times 2\times 17$
The common factors of the numbers 120 and 68 are 2 and 2.
The product of the common factors of the numbers 120 and 68 gives us the greatest common factor of 120 and 68
GCF of 120 and 68 is given by,
$\Rightarrow 2\times 2$
$\Rightarrow 4$
Therefore, the greatest common factor of the numbers 120 and 68 is 4.

Note: The greatest common factor of both the numbers is the greatest positive number that divides each of the numbers. The number 4 divides the numbers 120 and 68.
$\Rightarrow 120=4\times 30$
$\Rightarrow 68=4\times 17$
Hence this proves that the GCF of 120 and 68 is given by 4.