What is the Greatest Common Factor of 462 and 473?

Greatest common factor (GCF) of 462 and 473 is 11.

GCF(462,473) = 11

We will now calculate the prime factors of 462 and 473, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 462 and 473.

How to find the GCF of 462 and 473?

We will first find the prime factorization of 462 and 473. After we will calculate the factors of 462 and 473 and find the biggest common factor number .

Step-1: Prime Factorization of 462

Prime factors of 462 are 2, 3, 7, 11. Prime factorization of 462 in exponential form is:

462 = 2¹ × 3¹ × 7¹ × 11¹

Step-2: Prime Factorization of 473

Prime factors of 473 are 11, 43. Prime factorization of 473 in exponential form is:

473 = 11¹ × 43¹

Step-3: Factors of 462

List of positive integer factors of 462 that divides 462 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231

Step-4: Factors of 473

List of positive integer factors of 473 that divides 462 without a remainder.

1, 11, 43

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 462 and 473. The biggest common factor number is the GCF number.
So the greatest common factor 462 and 473 is 11.

Also check out the Least Common Multiple of 462 and 473