What is the Greatest Common Factor of 37632 and 37646?

Greatest common factor (GCF) of 37632 and 37646 is 14.

GCF(37632,37646) = 14

We will now calculate the prime factors of 37632 and 37646, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37632 and 37646.

How to find the GCF of 37632 and 37646?

We will first find the prime factorization of 37632 and 37646. After we will calculate the factors of 37632 and 37646 and find the biggest common factor number .

Step-1: Prime Factorization of 37632

Prime factors of 37632 are 2, 3, 7. Prime factorization of 37632 in exponential form is:

37632 = 2⁸ × 3¹ × 7²

Step-2: Prime Factorization of 37646

Prime factors of 37646 are 2, 7, 2689. Prime factorization of 37646 in exponential form is:

37646 = 2¹ × 7¹ × 2689¹

Step-3: Factors of 37632

List of positive integer factors of 37632 that divides 37632 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 49, 56, 64, 84, 96, 98, 112, 128, 147, 168, 192, 196, 224, 256, 294, 336, 384, 392, 448, 588, 672, 768, 784, 896, 1176, 1344, 1568, 1792, 2352, 2688, 3136, 4704, 5376, 6272, 9408, 12544, 18816

Step-4: Factors of 37646

List of positive integer factors of 37646 that divides 37632 without a remainder.

1, 2, 7, 14, 2689, 5378, 18823

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37632 and 37646. The biggest common factor number is the GCF number.
So the greatest common factor 37632 and 37646 is 14.

Also check out the Least Common Multiple of 37632 and 37646