What is the Greatest Common Factor of 31500 and 31518?

Greatest common factor (GCF) of 31500 and 31518 is 18.

GCF(31500,31518) = 18

We will now calculate the prime factors of 31500 and 31518, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31500 and 31518.

How to find the GCF of 31500 and 31518?

We will first find the prime factorization of 31500 and 31518. After we will calculate the factors of 31500 and 31518 and find the biggest common factor number .

Step-1: Prime Factorization of 31500

Prime factors of 31500 are 2, 3, 5, 7. Prime factorization of 31500 in exponential form is:

31500 = 2² × 3² × 5³ × 7¹

Step-2: Prime Factorization of 31518

Prime factors of 31518 are 2, 3, 17, 103. Prime factorization of 31518 in exponential form is:

31518 = 2¹ × 3² × 17¹ × 103¹

Step-3: Factors of 31500

List of positive integer factors of 31500 that divides 31500 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 125, 126, 140, 150, 175, 180, 210, 225, 250, 252, 300, 315, 350, 375, 420, 450, 500, 525, 630, 700, 750, 875, 900, 1050, 1125, 1260, 1500, 1575, 1750, 2100, 2250, 2625, 3150, 3500, 4500, 5250, 6300, 7875, 10500, 15750

Step-4: Factors of 31518

List of positive integer factors of 31518 that divides 31500 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 103, 153, 206, 306, 309, 618, 927, 1751, 1854, 3502, 5253, 10506, 15759

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31500 and 31518. The biggest common factor number is the GCF number.
So the greatest common factor 31500 and 31518 is 18.

Also check out the Least Common Multiple of 31500 and 31518