What is the Greatest Common Factor of 30719 and 30732?

Greatest common factor (GCF) of 30719 and 30732 is 13.

GCF(30719,30732) = 13

We will now calculate the prime factors of 30719 and 30732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30719 and 30732.

How to find the GCF of 30719 and 30732?

We will first find the prime factorization of 30719 and 30732. After we will calculate the factors of 30719 and 30732 and find the biggest common factor number .

Step-1: Prime Factorization of 30719

Prime factors of 30719 are 13, 17, 139. Prime factorization of 30719 in exponential form is:

30719 = 13¹ × 17¹ × 139¹

Step-2: Prime Factorization of 30732

Prime factors of 30732 are 2, 3, 13, 197. Prime factorization of 30732 in exponential form is:

30732 = 2² × 3¹ × 13¹ × 197¹

Step-3: Factors of 30719

List of positive integer factors of 30719 that divides 30719 without a remainder.

1, 13, 17, 139, 221, 1807, 2363

Step-4: Factors of 30732

List of positive integer factors of 30732 that divides 30719 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 197, 394, 591, 788, 1182, 2364, 2561, 5122, 7683, 10244, 15366

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30719 and 30732. The biggest common factor number is the GCF number.
So the greatest common factor 30719 and 30732 is 13.

Also check out the Least Common Multiple of 30719 and 30732