What is the Greatest Common Factor of 35280 and 35294?

Greatest common factor (GCF) of 35280 and 35294 is 14.

GCF(35280,35294) = 14

We will now calculate the prime factors of 35280 and 35294, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35280 and 35294.

How to find the GCF of 35280 and 35294?

We will first find the prime factorization of 35280 and 35294. After we will calculate the factors of 35280 and 35294 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 35294

Prime factors of 35294 are 2, 7, 2521. Prime factorization of 35294 in exponential form is:

35294 = 2¹ × 7¹ × 2521¹

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 35294

List of positive integer factors of 35294 that divides 35280 without a remainder.

1, 2, 7, 14, 2521, 5042, 17647

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35280 and 35294. The biggest common factor number is the GCF number.
So the greatest common factor 35280 and 35294 is 14.

Also check out the Least Common Multiple of 35280 and 35294