What is the Greatest Common Factor of 84315 and 84320?

Greatest common factor (GCF) of 84315 and 84320 is 5.

GCF(84315,84320) = 5

We will now calculate the prime factors of 84315 and 84320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84315 and 84320.

How to find the GCF of 84315 and 84320?

We will first find the prime factorization of 84315 and 84320. After we will calculate the factors of 84315 and 84320 and find the biggest common factor number .

Step-1: Prime Factorization of 84315

Prime factors of 84315 are 3, 5, 7, 11, 73. Prime factorization of 84315 in exponential form is:

84315 = 3¹ × 5¹ × 7¹ × 11¹ × 73¹

Step-2: Prime Factorization of 84320

Prime factors of 84320 are 2, 5, 17, 31. Prime factorization of 84320 in exponential form is:

84320 = 2⁵ × 5¹ × 17¹ × 31¹

Step-3: Factors of 84315

List of positive integer factors of 84315 that divides 84315 without a remainder.

1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 73, 77, 105, 165, 219, 231, 365, 385, 511, 803, 1095, 1155, 1533, 2409, 2555, 4015, 5621, 7665, 12045, 16863, 28105

Step-4: Factors of 84320

List of positive integer factors of 84320 that divides 84315 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 31, 32, 34, 40, 62, 68, 80, 85, 124, 136, 155, 160, 170, 248, 272, 310, 340, 496, 527, 544, 620, 680, 992, 1054, 1240, 1360, 2108, 2480, 2635, 2720, 4216, 4960, 5270, 8432, 10540, 16864, 21080, 42160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84315 and 84320. The biggest common factor number is the GCF number.
So the greatest common factor 84315 and 84320 is 5.

Also check out the Least Common Multiple of 84315 and 84320