What is the Greatest Common Factor of 31560 and 31578?

Greatest common factor (GCF) of 31560 and 31578 is 6.

GCF(31560,31578) = 6

We will now calculate the prime factors of 31560 and 31578, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31560 and 31578.

How to find the GCF of 31560 and 31578?

We will first find the prime factorization of 31560 and 31578. After we will calculate the factors of 31560 and 31578 and find the biggest common factor number .

Step-1: Prime Factorization of 31560

Prime factors of 31560 are 2, 3, 5, 263. Prime factorization of 31560 in exponential form is:

31560 = 2³ × 3¹ × 5¹ × 263¹

Step-2: Prime Factorization of 31578

Prime factors of 31578 are 2, 3, 19, 277. Prime factorization of 31578 in exponential form is:

31578 = 2¹ × 3¹ × 19¹ × 277¹

Step-3: Factors of 31560

List of positive integer factors of 31560 that divides 31560 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 263, 526, 789, 1052, 1315, 1578, 2104, 2630, 3156, 3945, 5260, 6312, 7890, 10520, 15780

Step-4: Factors of 31578

List of positive integer factors of 31578 that divides 31560 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 277, 554, 831, 1662, 5263, 10526, 15789

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31560 and 31578. The biggest common factor number is the GCF number.
So the greatest common factor 31560 and 31578 is 6.

Also check out the Least Common Multiple of 31560 and 31578