What is the Greatest Common Factor of 75974 and 75978?

Greatest common factor (GCF) of 75974 and 75978 is 2.

GCF(75974,75978) = 2

We will now calculate the prime factors of 75974 and 75978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75974 and 75978.

How to find the GCF of 75974 and 75978?

We will first find the prime factorization of 75974 and 75978. After we will calculate the factors of 75974 and 75978 and find the biggest common factor number .

Step-1: Prime Factorization of 75974

Prime factors of 75974 are 2, 37987. Prime factorization of 75974 in exponential form is:

75974 = 2¹ × 37987¹

Step-2: Prime Factorization of 75978

Prime factors of 75978 are 2, 3, 7, 67. Prime factorization of 75978 in exponential form is:

75978 = 2¹ × 3⁴ × 7¹ × 67¹

Step-3: Factors of 75974

List of positive integer factors of 75974 that divides 75974 without a remainder.

1, 2, 37987

Step-4: Factors of 75978

List of positive integer factors of 75978 that divides 75974 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 67, 81, 126, 134, 162, 189, 201, 378, 402, 469, 567, 603, 938, 1134, 1206, 1407, 1809, 2814, 3618, 4221, 5427, 8442, 10854, 12663, 25326, 37989

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75974 and 75978. The biggest common factor number is the GCF number.
So the greatest common factor 75974 and 75978 is 2.

Also check out the Least Common Multiple of 75974 and 75978