What is the Greatest Common Factor of 37632 and 37638?

Greatest common factor (GCF) of 37632 and 37638 is 6.

GCF(37632,37638) = 6

We will now calculate the prime factors of 37632 and 37638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37632 and 37638.

How to find the GCF of 37632 and 37638?

We will first find the prime factorization of 37632 and 37638. After we will calculate the factors of 37632 and 37638 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 37638

Prime factors of 37638 are 2, 3, 17, 41. Prime factorization of 37638 in exponential form is:

37638 = 2¹ × 3³ × 17¹ × 41¹

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 37638

List of positive integer factors of 37638 that divides 37632 without a remainder.

1, 2, 3, 6, 9, 17, 18, 27, 34, 41, 51, 54, 82, 102, 123, 153, 246, 306, 369, 459, 697, 738, 918, 1107, 1394, 2091, 2214, 4182, 6273, 12546, 18819

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37632 and 37638. The biggest common factor number is the GCF number.
So the greatest common factor 37632 and 37638 is 6.

Also check out the Least Common Multiple of 37632 and 37638