What is the Greatest Common Factor of 30672 and 30678?

Greatest common factor (GCF) of 30672 and 30678 is 6.

GCF(30672,30678) = 6

We will now calculate the prime factors of 30672 and 30678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30672 and 30678.

How to find the GCF of 30672 and 30678?

We will first find the prime factorization of 30672 and 30678. After we will calculate the factors of 30672 and 30678 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30678

Prime factors of 30678 are 2, 3, 5113. Prime factorization of 30678 in exponential form is:

30678 = 2¹ × 3¹ × 5113¹

Step-3: Factors of 30672

List of positive integer factors of 30672 that divides 30672 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

Step-4: Factors of 30678

List of positive integer factors of 30678 that divides 30672 without a remainder.

1, 2, 3, 6, 5113, 10226, 15339

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30672 and 30678. The biggest common factor number is the GCF number.
So the greatest common factor 30672 and 30678 is 6.

Also check out the Least Common Multiple of 30672 and 30678