What is the Greatest Common Factor of 1475 and 1480?

Greatest common factor (GCF) of 1475 and 1480 is 5.

GCF(1475,1480) = 5

We will now calculate the prime factors of 1475 and 1480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1475 and 1480.

How to find the GCF of 1475 and 1480?

We will first find the prime factorization of 1475 and 1480. After we will calculate the factors of 1475 and 1480 and find the biggest common factor number .

Step-1: Prime Factorization of 1475

Prime factors of 1475 are 5, 59. Prime factorization of 1475 in exponential form is:

1475 = 5² × 59¹

Step-2: Prime Factorization of 1480

Prime factors of 1480 are 2, 5, 37. Prime factorization of 1480 in exponential form is:

1480 = 2³ × 5¹ × 37¹

Step-3: Factors of 1475

List of positive integer factors of 1475 that divides 1475 without a remainder.

1, 5, 25, 59, 295

Step-4: Factors of 1480

List of positive integer factors of 1480 that divides 1475 without a remainder.

1, 2, 4, 5, 8, 10, 20, 37, 40, 74, 148, 185, 296, 370, 740

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1475 and 1480. The biggest common factor number is the GCF number.
So the greatest common factor 1475 and 1480 is 5.

Also check out the Least Common Multiple of 1475 and 1480