What is the Greatest Common Factor of 9975 and 9994?

Greatest common factor (GCF) of 9975 and 9994 is 19.

GCF(9975,9994) = 19

We will now calculate the prime factors of 9975 and 9994, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9975 and 9994.

How to find the GCF of 9975 and 9994?

We will first find the prime factorization of 9975 and 9994. After we will calculate the factors of 9975 and 9994 and find the biggest common factor number .

Step-1: Prime Factorization of 9975

Prime factors of 9975 are 3, 5, 7, 19. Prime factorization of 9975 in exponential form is:

9975 = 3¹ × 5² × 7¹ × 19¹

Step-2: Prime Factorization of 9994

Prime factors of 9994 are 2, 19, 263. Prime factorization of 9994 in exponential form is:

9994 = 2¹ × 19¹ × 263¹

Step-3: Factors of 9975

List of positive integer factors of 9975 that divides 9975 without a remainder.

1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325

Step-4: Factors of 9994

List of positive integer factors of 9994 that divides 9975 without a remainder.

1, 2, 19, 38, 263, 526, 4997

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9975 and 9994. The biggest common factor number is the GCF number.
So the greatest common factor 9975 and 9994 is 19.

Also check out the Least Common Multiple of 9975 and 9994