What is the Greatest Common Factor of 42945 and 42960?

Greatest common factor (GCF) of 42945 and 42960 is 15.

GCF(42945,42960) = 15

We will now calculate the prime factors of 42945 and 42960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42945 and 42960.

How to find the GCF of 42945 and 42960?

We will first find the prime factorization of 42945 and 42960. After we will calculate the factors of 42945 and 42960 and find the biggest common factor number .

Step-1: Prime Factorization of 42945

Prime factors of 42945 are 3, 5, 7, 409. Prime factorization of 42945 in exponential form is:

42945 = 3¹ × 5¹ × 7¹ × 409¹

Step-2: Prime Factorization of 42960

Prime factors of 42960 are 2, 3, 5, 179. Prime factorization of 42960 in exponential form is:

42960 = 2⁴ × 3¹ × 5¹ × 179¹

Step-3: Factors of 42945

List of positive integer factors of 42945 that divides 42945 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 409, 1227, 2045, 2863, 6135, 8589, 14315

Step-4: Factors of 42960

List of positive integer factors of 42960 that divides 42945 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 179, 240, 358, 537, 716, 895, 1074, 1432, 1790, 2148, 2685, 2864, 3580, 4296, 5370, 7160, 8592, 10740, 14320, 21480

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42945 and 42960. The biggest common factor number is the GCF number.
So the greatest common factor 42945 and 42960 is 15.

Also check out the Least Common Multiple of 42945 and 42960