What is the Greatest Common Factor of 37209 and 37224?

Greatest common factor (GCF) of 37209 and 37224 is 3.

GCF(37209,37224) = 3

We will now calculate the prime factors of 37209 and 37224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37209 and 37224.

How to find the GCF of 37209 and 37224?

We will first find the prime factorization of 37209 and 37224. After we will calculate the factors of 37209 and 37224 and find the biggest common factor number .

Step-1: Prime Factorization of 37209

Prime factors of 37209 are 3, 79, 157. Prime factorization of 37209 in exponential form is:

37209 = 3¹ × 79¹ × 157¹

Step-2: Prime Factorization of 37224

Prime factors of 37224 are 2, 3, 11, 47. Prime factorization of 37224 in exponential form is:

37224 = 2³ × 3² × 11¹ × 47¹

Step-3: Factors of 37209

List of positive integer factors of 37209 that divides 37209 without a remainder.

1, 3, 79, 157, 237, 471, 12403

Step-4: Factors of 37224

List of positive integer factors of 37224 that divides 37209 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 47, 66, 72, 88, 94, 99, 132, 141, 188, 198, 264, 282, 376, 396, 423, 517, 564, 792, 846, 1034, 1128, 1551, 1692, 2068, 3102, 3384, 4136, 4653, 6204, 9306, 12408, 18612

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37209 and 37224. The biggest common factor number is the GCF number.
So the greatest common factor 37209 and 37224 is 3.

Also check out the Least Common Multiple of 37209 and 37224