What is the Greatest Common Factor of 64380 and 64400?

Greatest common factor (GCF) of 64380 and 64400 is 20.

GCF(64380,64400) = 20

We will now calculate the prime factors of 64380 and 64400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64380 and 64400.

How to find the GCF of 64380 and 64400?

We will first find the prime factorization of 64380 and 64400. After we will calculate the factors of 64380 and 64400 and find the biggest common factor number .

Step-1: Prime Factorization of 64380

Prime factors of 64380 are 2, 3, 5, 29, 37. Prime factorization of 64380 in exponential form is:

64380 = 2² × 3¹ × 5¹ × 29¹ × 37¹

Step-2: Prime Factorization of 64400

Prime factors of 64400 are 2, 5, 7, 23. Prime factorization of 64400 in exponential form is:

64400 = 2⁴ × 5² × 7¹ × 23¹

Step-3: Factors of 64380

List of positive integer factors of 64380 that divides 64380 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 37, 58, 60, 74, 87, 111, 116, 145, 148, 174, 185, 222, 290, 348, 370, 435, 444, 555, 580, 740, 870, 1073, 1110, 1740, 2146, 2220, 3219, 4292, 5365, 6438, 10730, 12876, 16095, 21460, 32190

Step-4: Factors of 64400

List of positive integer factors of 64400 that divides 64380 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 23, 25, 28, 35, 40, 46, 50, 56, 70, 80, 92, 100, 112, 115, 140, 161, 175, 184, 200, 230, 280, 322, 350, 368, 400, 460, 560, 575, 644, 700, 805, 920, 1150, 1288, 1400, 1610, 1840, 2300, 2576, 2800, 3220, 4025, 4600, 6440, 8050, 9200, 12880, 16100, 32200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64380 and 64400. The biggest common factor number is the GCF number.
So the greatest common factor 64380 and 64400 is 20.

Also check out the Least Common Multiple of 64380 and 64400