What is the Greatest Common Factor of 31224 and 31234?

Greatest common factor (GCF) of 31224 and 31234 is 2.

GCF(31224,31234) = 2

We will now calculate the prime factors of 31224 and 31234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31224 and 31234.

How to find the GCF of 31224 and 31234?

We will first find the prime factorization of 31224 and 31234. After we will calculate the factors of 31224 and 31234 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31234

Prime factors of 31234 are 2, 7, 23, 97. Prime factorization of 31234 in exponential form is:

31234 = 2¹ × 7¹ × 23¹ × 97¹

Step-3: Factors of 31224

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

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

Step-4: Factors of 31234

List of positive integer factors of 31234 that divides 31224 without a remainder.

1, 2, 7, 14, 23, 46, 97, 161, 194, 322, 679, 1358, 2231, 4462, 15617

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31224 and 31234. The biggest common factor number is the GCF number.
So the greatest common factor 31224 and 31234 is 2.

Also check out the Least Common Multiple of 31224 and 31234