What is the Greatest Common Factor of 42705 and 42720?

Greatest common factor (GCF) of 42705 and 42720 is 15.

GCF(42705,42720) = 15

We will now calculate the prime factors of 42705 and 42720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42705 and 42720.

How to find the GCF of 42705 and 42720?

We will first find the prime factorization of 42705 and 42720. After we will calculate the factors of 42705 and 42720 and find the biggest common factor number .

Step-1: Prime Factorization of 42705

Prime factors of 42705 are 3, 5, 13, 73. Prime factorization of 42705 in exponential form is:

42705 = 3² × 5¹ × 13¹ × 73¹

Step-2: 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-3: Factors of 42705

List of positive integer factors of 42705 that divides 42705 without a remainder.

1, 3, 5, 9, 13, 15, 39, 45, 65, 73, 117, 195, 219, 365, 585, 657, 949, 1095, 2847, 3285, 4745, 8541, 14235

Step-4: Factors of 42720

List of positive integer factors of 42720 that divides 42705 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42705 and 42720. The biggest common factor number is the GCF number.
So the greatest common factor 42705 and 42720 is 15.

Also check out the Least Common Multiple of 42705 and 42720