What is the Greatest Common Factor of 23730 and 23742?

Greatest common factor (GCF) of 23730 and 23742 is 6.

GCF(23730,23742) = 6

We will now calculate the prime factors of 23730 and 23742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23730 and 23742.

How to find the GCF of 23730 and 23742?

We will first find the prime factorization of 23730 and 23742. After we will calculate the factors of 23730 and 23742 and find the biggest common factor number .

Step-1: Prime Factorization of 23730

Prime factors of 23730 are 2, 3, 5, 7, 113. Prime factorization of 23730 in exponential form is:

23730 = 2¹ × 3¹ × 5¹ × 7¹ × 113¹

Step-2: Prime Factorization of 23742

Prime factors of 23742 are 2, 3, 1319. Prime factorization of 23742 in exponential form is:

23742 = 2¹ × 3² × 1319¹

Step-3: Factors of 23730

List of positive integer factors of 23730 that divides 23730 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 113, 210, 226, 339, 565, 678, 791, 1130, 1582, 1695, 2373, 3390, 3955, 4746, 7910, 11865

Step-4: Factors of 23742

List of positive integer factors of 23742 that divides 23730 without a remainder.

1, 2, 3, 6, 9, 18, 1319, 2638, 3957, 7914, 11871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23730 and 23742. The biggest common factor number is the GCF number.
So the greatest common factor 23730 and 23742 is 6.

Also check out the Least Common Multiple of 23730 and 23742