What is the Greatest Common Factor of 31209 and 31224?

Greatest common factor (GCF) of 31209 and 31224 is 3.

GCF(31209,31224) = 3

We will now calculate the prime factors of 31209 and 31224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31209 and 31224.

How to find the GCF of 31209 and 31224?

We will first find the prime factorization of 31209 and 31224. After we will calculate the factors of 31209 and 31224 and find the biggest common factor number .

Step-1: Prime Factorization of 31209

Prime factors of 31209 are 3, 101, 103. Prime factorization of 31209 in exponential form is:

31209 = 3¹ × 101¹ × 103¹

Step-2: Prime Factorization of 31224

Prime factors of 31224 are 2, 3, 1301. Prime factorization of 31224 in exponential form is:

31224 = 2³ × 3¹ × 1301¹

Step-3: Factors of 31209

List of positive integer factors of 31209 that divides 31209 without a remainder.

1, 3, 101, 103, 303, 309, 10403

Step-4: Factors of 31224

List of positive integer factors of 31224 that divides 31209 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1301, 2602, 3903, 5204, 7806, 10408, 15612

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31209 and 31224. The biggest common factor number is the GCF number.
So the greatest common factor 31209 and 31224 is 3.

Also check out the Least Common Multiple of 31209 and 31224