What is the Greatest Common Factor of 30672 and 30688?

Greatest common factor (GCF) of 30672 and 30688 is 16.

GCF(30672,30688) = 16

We will now calculate the prime factors of 30672 and 30688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30672 and 30688.

How to find the GCF of 30672 and 30688?

We will first find the prime factorization of 30672 and 30688. After we will calculate the factors of 30672 and 30688 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 30688

Prime factors of 30688 are 2, 7, 137. Prime factorization of 30688 in exponential form is:

30688 = 2⁵ × 7¹ × 137¹

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 30688

List of positive integer factors of 30688 that divides 30672 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 137, 224, 274, 548, 959, 1096, 1918, 2192, 3836, 4384, 7672, 15344

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30672 and 30688. The biggest common factor number is the GCF number.
So the greatest common factor 30672 and 30688 is 16.

Also check out the Least Common Multiple of 30672 and 30688