What is the Greatest Common Factor of 442 and 460?

Greatest common factor (GCF) of 442 and 460 is 2.

GCF(442,460) = 2

We will now calculate the prime factors of 442 and 460, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 442 and 460.

How to find the GCF of 442 and 460?

We will first find the prime factorization of 442 and 460. After we will calculate the factors of 442 and 460 and find the biggest common factor number .

Step-1: Prime Factorization of 442

Prime factors of 442 are 2, 13, 17. Prime factorization of 442 in exponential form is:

442 = 2¹ × 13¹ × 17¹

Step-2: Prime Factorization of 460

Prime factors of 460 are 2, 5, 23. Prime factorization of 460 in exponential form is:

460 = 2² × 5¹ × 23¹

Step-3: Factors of 442

List of positive integer factors of 442 that divides 442 without a remainder.

1, 2, 13, 17, 26, 34, 221

Step-4: Factors of 460

List of positive integer factors of 460 that divides 442 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 442 and 460. The biggest common factor number is the GCF number.
So the greatest common factor 442 and 460 is 2.

Also check out the Least Common Multiple of 442 and 460