What is the Greatest Common Factor of 37740 and 37752?

Greatest common factor (GCF) of 37740 and 37752 is 12.

GCF(37740,37752) = 12

We will now calculate the prime factors of 37740 and 37752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37740 and 37752.

How to find the GCF of 37740 and 37752?

We will first find the prime factorization of 37740 and 37752. After we will calculate the factors of 37740 and 37752 and find the biggest common factor number .

Step-1: Prime Factorization of 37740

Prime factors of 37740 are 2, 3, 5, 17, 37. Prime factorization of 37740 in exponential form is:

37740 = 2² × 3¹ × 5¹ × 17¹ × 37¹

Step-2: Prime Factorization of 37752

Prime factors of 37752 are 2, 3, 11, 13. Prime factorization of 37752 in exponential form is:

37752 = 2³ × 3¹ × 11² × 13¹

Step-3: Factors of 37740

List of positive integer factors of 37740 that divides 37740 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 37, 51, 60, 68, 74, 85, 102, 111, 148, 170, 185, 204, 222, 255, 340, 370, 444, 510, 555, 629, 740, 1020, 1110, 1258, 1887, 2220, 2516, 3145, 3774, 6290, 7548, 9435, 12580, 18870

Step-4: Factors of 37752

List of positive integer factors of 37752 that divides 37740 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 13, 22, 24, 26, 33, 39, 44, 52, 66, 78, 88, 104, 121, 132, 143, 156, 242, 264, 286, 312, 363, 429, 484, 572, 726, 858, 968, 1144, 1452, 1573, 1716, 2904, 3146, 3432, 4719, 6292, 9438, 12584, 18876

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37740 and 37752. The biggest common factor number is the GCF number.
So the greatest common factor 37740 and 37752 is 12.

Also check out the Least Common Multiple of 37740 and 37752