What is the Greatest Common Factor of 42960 and 42978?

Greatest common factor (GCF) of 42960 and 42978 is 6.

GCF(42960,42978) = 6

We will now calculate the prime factors of 42960 and 42978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42960 and 42978.

How to find the GCF of 42960 and 42978?

We will first find the prime factorization of 42960 and 42978. After we will calculate the factors of 42960 and 42978 and find the biggest common factor number .

Step-1: Prime Factorization of 42960

Prime factors of 42960 are 2, 3, 5, 179. Prime factorization of 42960 in exponential form is:

42960 = 2⁴ × 3¹ × 5¹ × 179¹

Step-2: Prime Factorization of 42978

Prime factors of 42978 are 2, 3, 13, 19, 29. Prime factorization of 42978 in exponential form is:

42978 = 2¹ × 3¹ × 13¹ × 19¹ × 29¹

Step-3: Factors of 42960

List of positive integer factors of 42960 that divides 42960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 179, 240, 358, 537, 716, 895, 1074, 1432, 1790, 2148, 2685, 2864, 3580, 4296, 5370, 7160, 8592, 10740, 14320, 21480

Step-4: Factors of 42978

List of positive integer factors of 42978 that divides 42960 without a remainder.

1, 2, 3, 6, 13, 19, 26, 29, 38, 39, 57, 58, 78, 87, 114, 174, 247, 377, 494, 551, 741, 754, 1102, 1131, 1482, 1653, 2262, 3306, 7163, 14326, 21489

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42960 and 42978. The biggest common factor number is the GCF number.
So the greatest common factor 42960 and 42978 is 6.

Also check out the Least Common Multiple of 42960 and 42978