What is the Greatest Common Factor of 39130 and 39144?

Greatest common factor (GCF) of 39130 and 39144 is 14.

GCF(39130,39144) = 14

We will now calculate the prime factors of 39130 and 39144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39130 and 39144.

How to find the GCF of 39130 and 39144?

We will first find the prime factorization of 39130 and 39144. After we will calculate the factors of 39130 and 39144 and find the biggest common factor number .

Step-1: Prime Factorization of 39130

Prime factors of 39130 are 2, 5, 7, 13, 43. Prime factorization of 39130 in exponential form is:

39130 = 2¹ × 5¹ × 7¹ × 13¹ × 43¹

Step-2: Prime Factorization of 39144

Prime factors of 39144 are 2, 3, 7, 233. Prime factorization of 39144 in exponential form is:

39144 = 2³ × 3¹ × 7¹ × 233¹

Step-3: Factors of 39130

List of positive integer factors of 39130 that divides 39130 without a remainder.

1, 2, 5, 7, 10, 13, 14, 26, 35, 43, 65, 70, 86, 91, 130, 182, 215, 301, 430, 455, 559, 602, 910, 1118, 1505, 2795, 3010, 3913, 5590, 7826, 19565

Step-4: Factors of 39144

List of positive integer factors of 39144 that divides 39130 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168, 233, 466, 699, 932, 1398, 1631, 1864, 2796, 3262, 4893, 5592, 6524, 9786, 13048, 19572

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39130 and 39144. The biggest common factor number is the GCF number.
So the greatest common factor 39130 and 39144 is 14.

Also check out the Least Common Multiple of 39130 and 39144