What is the Greatest Common Factor of 37996 and 38010?

Greatest common factor (GCF) of 37996 and 38010 is 14.

GCF(37996,38010) = 14

We will now calculate the prime factors of 37996 and 38010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37996 and 38010.

How to find the GCF of 37996 and 38010?

We will first find the prime factorization of 37996 and 38010. After we will calculate the factors of 37996 and 38010 and find the biggest common factor number .

Step-1: Prime Factorization of 37996

Prime factors of 37996 are 2, 7, 23, 59. Prime factorization of 37996 in exponential form is:

37996 = 2² × 7¹ × 23¹ × 59¹

Step-2: Prime Factorization of 38010

Prime factors of 38010 are 2, 3, 5, 7, 181. Prime factorization of 38010 in exponential form is:

38010 = 2¹ × 3¹ × 5¹ × 7¹ × 181¹

Step-3: Factors of 37996

List of positive integer factors of 37996 that divides 37996 without a remainder.

1, 2, 4, 7, 14, 23, 28, 46, 59, 92, 118, 161, 236, 322, 413, 644, 826, 1357, 1652, 2714, 5428, 9499, 18998

Step-4: Factors of 38010

List of positive integer factors of 38010 that divides 37996 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 181, 210, 362, 543, 905, 1086, 1267, 1810, 2534, 2715, 3801, 5430, 6335, 7602, 12670, 19005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37996 and 38010. The biggest common factor number is the GCF number.
So the greatest common factor 37996 and 38010 is 14.

Also check out the Least Common Multiple of 37996 and 38010