What is the Greatest Common Factor of 35280 and 35300?

Greatest common factor (GCF) of 35280 and 35300 is 20.

GCF(35280,35300) = 20

We will now calculate the prime factors of 35280 and 35300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35280 and 35300.

How to find the GCF of 35280 and 35300?

We will first find the prime factorization of 35280 and 35300. After we will calculate the factors of 35280 and 35300 and find the biggest common factor number .

Step-1: Prime Factorization of 35280

Prime factors of 35280 are 2, 3, 5, 7. Prime factorization of 35280 in exponential form is:

35280 = 2⁴ × 3² × 5¹ × 7²

Step-2: Prime Factorization of 35300

Prime factors of 35300 are 2, 5, 353. Prime factorization of 35300 in exponential form is:

35300 = 2² × 5² × 353¹

Step-3: Factors of 35280

List of positive integer factors of 35280 that divides 35280 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 49, 56, 60, 63, 70, 72, 80, 84, 90, 98, 105, 112, 120, 126, 140, 144, 147, 168, 180, 196, 210, 240, 245, 252, 280, 294, 315, 336, 360, 392, 420, 441, 490, 504, 560, 588, 630, 720, 735, 784, 840, 882, 980, 1008, 1176, 1260, 1470, 1680, 1764, 1960, 2205, 2352, 2520, 2940, 3528, 3920, 4410, 5040, 5880, 7056, 8820, 11760, 17640

Step-4: Factors of 35300

List of positive integer factors of 35300 that divides 35280 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 353, 706, 1412, 1765, 3530, 7060, 8825, 17650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35280 and 35300. The biggest common factor number is the GCF number.
So the greatest common factor 35280 and 35300 is 20.

Also check out the Least Common Multiple of 35280 and 35300