What is the Greatest Common Factor of 37808 and 37825?

Greatest common factor (GCF) of 37808 and 37825 is 17.

GCF(37808,37825) = 17

We will now calculate the prime factors of 37808 and 37825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37808 and 37825.

How to find the GCF of 37808 and 37825?

We will first find the prime factorization of 37808 and 37825. After we will calculate the factors of 37808 and 37825 and find the biggest common factor number .

Step-1: Prime Factorization of 37808

Prime factors of 37808 are 2, 17, 139. Prime factorization of 37808 in exponential form is:

37808 = 2⁴ × 17¹ × 139¹

Step-2: Prime Factorization of 37825

Prime factors of 37825 are 5, 17, 89. Prime factorization of 37825 in exponential form is:

37825 = 5² × 17¹ × 89¹

Step-3: Factors of 37808

List of positive integer factors of 37808 that divides 37808 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 139, 272, 278, 556, 1112, 2224, 2363, 4726, 9452, 18904

Step-4: Factors of 37825

List of positive integer factors of 37825 that divides 37808 without a remainder.

1, 5, 17, 25, 85, 89, 425, 445, 1513, 2225, 7565

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37808 and 37825. The biggest common factor number is the GCF number.
So the greatest common factor 37808 and 37825 is 17.

Also check out the Least Common Multiple of 37808 and 37825