What is the Greatest Common Factor of 75972 and 75978?

Greatest common factor (GCF) of 75972 and 75978 is 6.

GCF(75972,75978) = 6

We will now calculate the prime factors of 75972 and 75978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75972 and 75978.

How to find the GCF of 75972 and 75978?

We will first find the prime factorization of 75972 and 75978. After we will calculate the factors of 75972 and 75978 and find the biggest common factor number .

Step-1: Prime Factorization of 75972

Prime factors of 75972 are 2, 3, 13, 487. Prime factorization of 75972 in exponential form is:

75972 = 2² × 3¹ × 13¹ × 487¹

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 75972

List of positive integer factors of 75972 that divides 75972 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 487, 974, 1461, 1948, 2922, 5844, 6331, 12662, 18993, 25324, 37986

Step-4: Factors of 75978

List of positive integer factors of 75978 that divides 75972 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 75972 and 75978. The biggest common factor number is the GCF number.
So the greatest common factor 75972 and 75978 is 6.

Also check out the Least Common Multiple of 75972 and 75978