What is the Greatest Common Factor of 36945 and 36960?

Greatest common factor (GCF) of 36945 and 36960 is 15.

GCF(36945,36960) = 15

We will now calculate the prime factors of 36945 and 36960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36945 and 36960.

How to find the GCF of 36945 and 36960?

We will first find the prime factorization of 36945 and 36960. After we will calculate the factors of 36945 and 36960 and find the biggest common factor number .

Step-1: Prime Factorization of 36945

Prime factors of 36945 are 3, 5, 821. Prime factorization of 36945 in exponential form is:

36945 = 3² × 5¹ × 821¹

Step-2: Prime Factorization of 36960

Prime factors of 36960 are 2, 3, 5, 7, 11. Prime factorization of 36960 in exponential form is:

36960 = 2⁵ × 3¹ × 5¹ × 7¹ × 11¹

Step-3: Factors of 36945

List of positive integer factors of 36945 that divides 36945 without a remainder.

1, 3, 5, 9, 15, 45, 821, 2463, 4105, 7389, 12315

Step-4: Factors of 36960

List of positive integer factors of 36960 that divides 36945 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 20, 21, 22, 24, 28, 30, 32, 33, 35, 40, 42, 44, 48, 55, 56, 60, 66, 70, 77, 80, 84, 88, 96, 105, 110, 112, 120, 132, 140, 154, 160, 165, 168, 176, 210, 220, 224, 231, 240, 264, 280, 308, 330, 336, 352, 385, 420, 440, 462, 480, 528, 560, 616, 660, 672, 770, 840, 880, 924, 1056, 1120, 1155, 1232, 1320, 1540, 1680, 1760, 1848, 2310, 2464, 2640, 3080, 3360, 3696, 4620, 5280, 6160, 7392, 9240, 12320, 18480

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36945 and 36960. The biggest common factor number is the GCF number.
So the greatest common factor 36945 and 36960 is 15.

Also check out the Least Common Multiple of 36945 and 36960