What is the Greatest Common Factor of 39712 and 39730?

Greatest common factor (GCF) of 39712 and 39730 is 2.

GCF(39712,39730) = 2

We will now calculate the prime factors of 39712 and 39730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39712 and 39730.

How to find the GCF of 39712 and 39730?

We will first find the prime factorization of 39712 and 39730. After we will calculate the factors of 39712 and 39730 and find the biggest common factor number .

Step-1: Prime Factorization of 39712

Prime factors of 39712 are 2, 17, 73. Prime factorization of 39712 in exponential form is:

39712 = 2⁵ × 17¹ × 73¹

Step-2: Prime Factorization of 39730

Prime factors of 39730 are 2, 5, 29, 137. Prime factorization of 39730 in exponential form is:

39730 = 2¹ × 5¹ × 29¹ × 137¹

Step-3: Factors of 39712

List of positive integer factors of 39712 that divides 39712 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 68, 73, 136, 146, 272, 292, 544, 584, 1168, 1241, 2336, 2482, 4964, 9928, 19856

Step-4: Factors of 39730

List of positive integer factors of 39730 that divides 39712 without a remainder.

1, 2, 5, 10, 29, 58, 137, 145, 274, 290, 685, 1370, 3973, 7946, 19865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39712 and 39730. The biggest common factor number is the GCF number.
So the greatest common factor 39712 and 39730 is 2.

Also check out the Least Common Multiple of 39712 and 39730