What is the Greatest Common Factor of 31290 and 31300?

Greatest common factor (GCF) of 31290 and 31300 is 10.

GCF(31290,31300) = 10

We will now calculate the prime factors of 31290 and 31300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31290 and 31300.

How to find the GCF of 31290 and 31300?

We will first find the prime factorization of 31290 and 31300. After we will calculate the factors of 31290 and 31300 and find the biggest common factor number .

Step-1: Prime Factorization of 31290

Prime factors of 31290 are 2, 3, 5, 7, 149. Prime factorization of 31290 in exponential form is:

31290 = 2¹ × 3¹ × 5¹ × 7¹ × 149¹

Step-2: 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-3: Factors of 31290

List of positive integer factors of 31290 that divides 31290 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 149, 210, 298, 447, 745, 894, 1043, 1490, 2086, 2235, 3129, 4470, 5215, 6258, 10430, 15645

Step-4: Factors of 31300

List of positive integer factors of 31300 that divides 31290 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31290 and 31300. The biggest common factor number is the GCF number.
So the greatest common factor 31290 and 31300 is 10.

Also check out the Least Common Multiple of 31290 and 31300