What is the Greatest Common Factor of 37745 and 37760?

Greatest common factor (GCF) of 37745 and 37760 is 5.

GCF(37745,37760) = 5

We will now calculate the prime factors of 37745 and 37760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37745 and 37760.

How to find the GCF of 37745 and 37760?

We will first find the prime factorization of 37745 and 37760. After we will calculate the factors of 37745 and 37760 and find the biggest common factor number .

Step-1: Prime Factorization of 37745

Prime factors of 37745 are 5, 7549. Prime factorization of 37745 in exponential form is:

37745 = 5¹ × 7549¹

Step-2: Prime Factorization of 37760

Prime factors of 37760 are 2, 5, 59. Prime factorization of 37760 in exponential form is:

37760 = 2⁷ × 5¹ × 59¹

Step-3: Factors of 37745

List of positive integer factors of 37745 that divides 37745 without a remainder.

1, 5, 7549

Step-4: Factors of 37760

List of positive integer factors of 37760 that divides 37745 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 59, 64, 80, 118, 128, 160, 236, 295, 320, 472, 590, 640, 944, 1180, 1888, 2360, 3776, 4720, 7552, 9440, 18880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37745 and 37760. The biggest common factor number is the GCF number.
So the greatest common factor 37745 and 37760 is 5.

Also check out the Least Common Multiple of 37745 and 37760