What is the Greatest Common Factor of 37625 and 37632?

Greatest common factor (GCF) of 37625 and 37632 is 7.

GCF(37625,37632) = 7

We will now calculate the prime factors of 37625 and 37632, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37625 and 37632.

How to find the GCF of 37625 and 37632?

We will first find the prime factorization of 37625 and 37632. After we will calculate the factors of 37625 and 37632 and find the biggest common factor number .

Step-1: Prime Factorization of 37625

Prime factors of 37625 are 5, 7, 43. Prime factorization of 37625 in exponential form is:

37625 = 5³ × 7¹ × 43¹

Step-2: 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-3: Factors of 37625

List of positive integer factors of 37625 that divides 37625 without a remainder.

1, 5, 7, 25, 35, 43, 125, 175, 215, 301, 875, 1075, 1505, 5375, 7525

Step-4: Factors of 37632

List of positive integer factors of 37632 that divides 37625 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37625 and 37632. The biggest common factor number is the GCF number.
So the greatest common factor 37625 and 37632 is 7.

Also check out the Least Common Multiple of 37625 and 37632