What is the Greatest Common Factor of 70065 and 70080?

Greatest common factor (GCF) of 70065 and 70080 is 15.

GCF(70065,70080) = 15

We will now calculate the prime factors of 70065 and 70080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70065 and 70080.

How to find the GCF of 70065 and 70080?

We will first find the prime factorization of 70065 and 70080. After we will calculate the factors of 70065 and 70080 and find the biggest common factor number .

Step-1: Prime Factorization of 70065

Prime factors of 70065 are 3, 5, 173. Prime factorization of 70065 in exponential form is:

70065 = 3⁴ × 5¹ × 173¹

Step-2: Prime Factorization of 70080

Prime factors of 70080 are 2, 3, 5, 73. Prime factorization of 70080 in exponential form is:

70080 = 2⁶ × 3¹ × 5¹ × 73¹

Step-3: Factors of 70065

List of positive integer factors of 70065 that divides 70065 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 135, 173, 405, 519, 865, 1557, 2595, 4671, 7785, 14013, 23355

Step-4: Factors of 70080

List of positive integer factors of 70080 that divides 70065 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 73, 80, 96, 120, 146, 160, 192, 219, 240, 292, 320, 365, 438, 480, 584, 730, 876, 960, 1095, 1168, 1460, 1752, 2190, 2336, 2920, 3504, 4380, 4672, 5840, 7008, 8760, 11680, 14016, 17520, 23360, 35040

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70065 and 70080. The biggest common factor number is the GCF number.
So the greatest common factor 70065 and 70080 is 15.

Also check out the Least Common Multiple of 70065 and 70080