What is the Greatest Common Factor of 1410 and 1425?

Greatest common factor (GCF) of 1410 and 1425 is 15.

GCF(1410,1425) = 15

We will now calculate the prime factors of 1410 and 1425, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1410 and 1425.

How to find the GCF of 1410 and 1425?

We will first find the prime factorization of 1410 and 1425. After we will calculate the factors of 1410 and 1425 and find the biggest common factor number .

Step-1: Prime Factorization of 1410

Prime factors of 1410 are 2, 3, 5, 47. Prime factorization of 1410 in exponential form is:

1410 = 2¹ × 3¹ × 5¹ × 47¹

Step-2: Prime Factorization of 1425

Prime factors of 1425 are 3, 5, 19. Prime factorization of 1425 in exponential form is:

1425 = 3¹ × 5² × 19¹

Step-3: Factors of 1410

List of positive integer factors of 1410 that divides 1410 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705

Step-4: Factors of 1425

List of positive integer factors of 1425 that divides 1410 without a remainder.

1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 475

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1410 and 1425. The biggest common factor number is the GCF number.
So the greatest common factor 1410 and 1425 is 15.

Also check out the Least Common Multiple of 1410 and 1425