What is the Greatest Common Factor of 39962 and 39975?

Greatest common factor (GCF) of 39962 and 39975 is 13.

GCF(39962,39975) = 13

We will now calculate the prime factors of 39962 and 39975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39962 and 39975.

How to find the GCF of 39962 and 39975?

We will first find the prime factorization of 39962 and 39975. After we will calculate the factors of 39962 and 39975 and find the biggest common factor number .

Step-1: Prime Factorization of 39962

Prime factors of 39962 are 2, 13, 29, 53. Prime factorization of 39962 in exponential form is:

39962 = 2¹ × 13¹ × 29¹ × 53¹

Step-2: Prime Factorization of 39975

Prime factors of 39975 are 3, 5, 13, 41. Prime factorization of 39975 in exponential form is:

39975 = 3¹ × 5² × 13¹ × 41¹

Step-3: Factors of 39962

List of positive integer factors of 39962 that divides 39962 without a remainder.

1, 2, 13, 26, 29, 53, 58, 106, 377, 689, 754, 1378, 1537, 3074, 19981

Step-4: Factors of 39975

List of positive integer factors of 39975 that divides 39962 without a remainder.

1, 3, 5, 13, 15, 25, 39, 41, 65, 75, 123, 195, 205, 325, 533, 615, 975, 1025, 1599, 2665, 3075, 7995, 13325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39962 and 39975. The biggest common factor number is the GCF number.
So the greatest common factor 39962 and 39975 is 13.

Also check out the Least Common Multiple of 39962 and 39975