What is the Greatest Common Factor of 37742 and 37760?

Greatest common factor (GCF) of 37742 and 37760 is 2.

GCF(37742,37760) = 2

We will now calculate the prime factors of 37742 and 37760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37742 and 37760.

How to find the GCF of 37742 and 37760?

We will first find the prime factorization of 37742 and 37760. After we will calculate the factors of 37742 and 37760 and find the biggest common factor number .

Step-1: Prime Factorization of 37742

Prime factors of 37742 are 2, 113, 167. Prime factorization of 37742 in exponential form is:

37742 = 2¹ × 113¹ × 167¹

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 37742

List of positive integer factors of 37742 that divides 37742 without a remainder.

1, 2, 113, 167, 226, 334, 18871

Step-4: Factors of 37760

List of positive integer factors of 37760 that divides 37742 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 37742 and 37760. The biggest common factor number is the GCF number.
So the greatest common factor 37742 and 37760 is 2.

Also check out the Least Common Multiple of 37742 and 37760