What is the Greatest Common Factor of 30714 and 30732?

Greatest common factor (GCF) of 30714 and 30732 is 6.

GCF(30714,30732) = 6

We will now calculate the prime factors of 30714 and 30732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30714 and 30732.

How to find the GCF of 30714 and 30732?

We will first find the prime factorization of 30714 and 30732. After we will calculate the factors of 30714 and 30732 and find the biggest common factor number .

Step-1: Prime Factorization of 30714

Prime factors of 30714 are 2, 3, 5119. Prime factorization of 30714 in exponential form is:

30714 = 2¹ × 3¹ × 5119¹

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 30714

List of positive integer factors of 30714 that divides 30714 without a remainder.

1, 2, 3, 6, 5119, 10238, 15357

Step-4: Factors of 30732

List of positive integer factors of 30732 that divides 30714 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 30714 and 30732. The biggest common factor number is the GCF number.
So the greatest common factor 30714 and 30732 is 6.

Also check out the Least Common Multiple of 30714 and 30732