What is the Greatest Common Factor of 71825 and 71838?

Greatest common factor (GCF) of 71825 and 71838 is 13.

GCF(71825,71838) = 13

We will now calculate the prime factors of 71825 and 71838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71825 and 71838.

How to find the GCF of 71825 and 71838?

We will first find the prime factorization of 71825 and 71838. After we will calculate the factors of 71825 and 71838 and find the biggest common factor number .

Step-1: Prime Factorization of 71825

Prime factors of 71825 are 5, 13, 17. Prime factorization of 71825 in exponential form is:

71825 = 5² × 13² × 17¹

Step-2: Prime Factorization of 71838

Prime factors of 71838 are 2, 3, 13, 307. Prime factorization of 71838 in exponential form is:

71838 = 2¹ × 3² × 13¹ × 307¹

Step-3: Factors of 71825

List of positive integer factors of 71825 that divides 71825 without a remainder.

1, 5, 13, 17, 25, 65, 85, 169, 221, 325, 425, 845, 1105, 2873, 4225, 5525, 14365

Step-4: Factors of 71838

List of positive integer factors of 71838 that divides 71825 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234, 307, 614, 921, 1842, 2763, 3991, 5526, 7982, 11973, 23946, 35919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71825 and 71838. The biggest common factor number is the GCF number.
So the greatest common factor 71825 and 71838 is 13.

Also check out the Least Common Multiple of 71825 and 71838