What is the Greatest Common Factor of 465 and 473?

Greatest common factor (GCF) of 465 and 473 is 1.

GCF(465,473) = 1

We will now calculate the prime factors of 465 and 473, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 465 and 473.

How to find the GCF of 465 and 473?

We will first find the prime factorization of 465 and 473. After we will calculate the factors of 465 and 473 and find the biggest common factor number .

Step-1: Prime Factorization of 465

Prime factors of 465 are 3, 5, 31. Prime factorization of 465 in exponential form is:

465 = 3¹ × 5¹ × 31¹

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 465

List of positive integer factors of 465 that divides 465 without a remainder.

1, 3, 5, 15, 31, 93, 155

Step-4: Factors of 473

List of positive integer factors of 473 that divides 465 without a remainder.

1, 11, 43

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 465 and 473. The biggest common factor number is the GCF number.
So the greatest common factor 465 and 473 is 1.

Also check out the Least Common Multiple of 465 and 473