What is the Greatest Common Factor of 31300 and 31320?

Greatest common factor (GCF) of 31300 and 31320 is 20.

GCF(31300,31320) = 20

We will now calculate the prime factors of 31300 and 31320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31300 and 31320.

How to find the GCF of 31300 and 31320?

We will first find the prime factorization of 31300 and 31320. After we will calculate the factors of 31300 and 31320 and find the biggest common factor number .

Step-1: Prime Factorization of 31300

Prime factors of 31300 are 2, 5, 313. Prime factorization of 31300 in exponential form is:

31300 = 2² × 5² × 313¹

Step-2: Prime Factorization of 31320

Prime factors of 31320 are 2, 3, 5, 29. Prime factorization of 31320 in exponential form is:

31320 = 2³ × 3³ × 5¹ × 29¹

Step-3: Factors of 31300

List of positive integer factors of 31300 that divides 31300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 313, 626, 1252, 1565, 3130, 6260, 7825, 15650

Step-4: Factors of 31320

List of positive integer factors of 31320 that divides 31300 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 29, 30, 36, 40, 45, 54, 58, 60, 72, 87, 90, 108, 116, 120, 135, 145, 174, 180, 216, 232, 261, 270, 290, 348, 360, 435, 522, 540, 580, 696, 783, 870, 1044, 1080, 1160, 1305, 1566, 1740, 2088, 2610, 3132, 3480, 3915, 5220, 6264, 7830, 10440, 15660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31300 and 31320. The biggest common factor number is the GCF number.
So the greatest common factor 31300 and 31320 is 20.

Also check out the Least Common Multiple of 31300 and 31320