What is the Greatest Common Factor of 78960 and 78972?

Greatest common factor (GCF) of 78960 and 78972 is 12.

GCF(78960,78972) = 12

We will now calculate the prime factors of 78960 and 78972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78960 and 78972.

How to find the GCF of 78960 and 78972?

We will first find the prime factorization of 78960 and 78972. After we will calculate the factors of 78960 and 78972 and find the biggest common factor number .

Step-1: Prime Factorization of 78960

Prime factors of 78960 are 2, 3, 5, 7, 47. Prime factorization of 78960 in exponential form is:

78960 = 2⁴ × 3¹ × 5¹ × 7¹ × 47¹

Step-2: Prime Factorization of 78972

Prime factors of 78972 are 2, 3, 6581. Prime factorization of 78972 in exponential form is:

78972 = 2² × 3¹ × 6581¹

Step-3: Factors of 78960

List of positive integer factors of 78960 that divides 78960 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 47, 48, 56, 60, 70, 80, 84, 94, 105, 112, 120, 140, 141, 168, 188, 210, 235, 240, 280, 282, 329, 336, 376, 420, 470, 560, 564, 658, 705, 752, 840, 940, 987, 1128, 1316, 1410, 1645, 1680, 1880, 1974, 2256, 2632, 2820, 3290, 3760, 3948, 4935, 5264, 5640, 6580, 7896, 9870, 11280, 13160, 15792, 19740, 26320, 39480

Step-4: Factors of 78972

List of positive integer factors of 78972 that divides 78960 without a remainder.

1, 2, 3, 4, 6, 12, 6581, 13162, 19743, 26324, 39486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78960 and 78972. The biggest common factor number is the GCF number.
So the greatest common factor 78960 and 78972 is 12.

Also check out the Least Common Multiple of 78960 and 78972