What is the Greatest Common Factor of 37680 and 37696?

Greatest common factor (GCF) of 37680 and 37696 is 16.

GCF(37680,37696) = 16

We will now calculate the prime factors of 37680 and 37696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37680 and 37696.

How to find the GCF of 37680 and 37696?

We will first find the prime factorization of 37680 and 37696. After we will calculate the factors of 37680 and 37696 and find the biggest common factor number .

Step-1: Prime Factorization of 37680

Prime factors of 37680 are 2, 3, 5, 157. Prime factorization of 37680 in exponential form is:

37680 = 2⁴ × 3¹ × 5¹ × 157¹

Step-2: Prime Factorization of 37696

Prime factors of 37696 are 2, 19, 31. Prime factorization of 37696 in exponential form is:

37696 = 2⁶ × 19¹ × 31¹

Step-3: Factors of 37680

List of positive integer factors of 37680 that divides 37680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 157, 240, 314, 471, 628, 785, 942, 1256, 1570, 1884, 2355, 2512, 3140, 3768, 4710, 6280, 7536, 9420, 12560, 18840

Step-4: Factors of 37696

List of positive integer factors of 37696 that divides 37680 without a remainder.

1, 2, 4, 8, 16, 19, 31, 32, 38, 62, 64, 76, 124, 152, 248, 304, 496, 589, 608, 992, 1178, 1216, 1984, 2356, 4712, 9424, 18848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37680 and 37696. The biggest common factor number is the GCF number.
So the greatest common factor 37680 and 37696 is 16.

Also check out the Least Common Multiple of 37680 and 37696