What is the Greatest Common Factor of 30657 and 30672?

Greatest common factor (GCF) of 30657 and 30672 is 3.

GCF(30657,30672) = 3

We will now calculate the prime factors of 30657 and 30672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30657 and 30672.

How to find the GCF of 30657 and 30672?

We will first find the prime factorization of 30657 and 30672. After we will calculate the factors of 30657 and 30672 and find the biggest common factor number .

Step-1: Prime Factorization of 30657

Prime factors of 30657 are 3, 11, 929. Prime factorization of 30657 in exponential form is:

30657 = 3¹ × 11¹ × 929¹

Step-2: Prime Factorization of 30672

Prime factors of 30672 are 2, 3, 71. Prime factorization of 30672 in exponential form is:

30672 = 2⁴ × 3³ × 71¹

Step-3: Factors of 30657

List of positive integer factors of 30657 that divides 30657 without a remainder.

1, 3, 11, 33, 929, 2787, 10219

Step-4: Factors of 30672

List of positive integer factors of 30672 that divides 30657 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 71, 72, 108, 142, 144, 213, 216, 284, 426, 432, 568, 639, 852, 1136, 1278, 1704, 1917, 2556, 3408, 3834, 5112, 7668, 10224, 15336

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30657 and 30672. The biggest common factor number is the GCF number.
So the greatest common factor 30657 and 30672 is 3.

Also check out the Least Common Multiple of 30657 and 30672