What is the Greatest Common Factor of 42720 and 42735?

Greatest common factor (GCF) of 42720 and 42735 is 15.

GCF(42720,42735) = 15

We will now calculate the prime factors of 42720 and 42735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42720 and 42735.

How to find the GCF of 42720 and 42735?

We will first find the prime factorization of 42720 and 42735. After we will calculate the factors of 42720 and 42735 and find the biggest common factor number .

Step-1: Prime Factorization of 42720

Prime factors of 42720 are 2, 3, 5, 89. Prime factorization of 42720 in exponential form is:

42720 = 2⁵ × 3¹ × 5¹ × 89¹

Step-2: Prime Factorization of 42735

Prime factors of 42735 are 3, 5, 7, 11, 37. Prime factorization of 42735 in exponential form is:

42735 = 3¹ × 5¹ × 7¹ × 11¹ × 37¹

Step-3: Factors of 42720

List of positive integer factors of 42720 that divides 42720 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 89, 96, 120, 160, 178, 240, 267, 356, 445, 480, 534, 712, 890, 1068, 1335, 1424, 1780, 2136, 2670, 2848, 3560, 4272, 5340, 7120, 8544, 10680, 14240, 21360

Step-4: Factors of 42735

List of positive integer factors of 42735 that divides 42720 without a remainder.

1, 3, 5, 7, 11, 15, 21, 33, 35, 37, 55, 77, 105, 111, 165, 185, 231, 259, 385, 407, 555, 777, 1155, 1221, 1295, 2035, 2849, 3885, 6105, 8547, 14245

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42720 and 42735. The biggest common factor number is the GCF number.
So the greatest common factor 42720 and 42735 is 15.

Also check out the Least Common Multiple of 42720 and 42735