What is the Greatest Common Factor of 1407 and 1413?

Greatest common factor (GCF) of 1407 and 1413 is 3.

GCF(1407,1413) = 3

We will now calculate the prime factors of 1407 and 1413, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1407 and 1413.

How to find the GCF of 1407 and 1413?

We will first find the prime factorization of 1407 and 1413. After we will calculate the factors of 1407 and 1413 and find the biggest common factor number .

Step-1: Prime Factorization of 1407

Prime factors of 1407 are 3, 7, 67. Prime factorization of 1407 in exponential form is:

1407 = 3¹ × 7¹ × 67¹

Step-2: Prime Factorization of 1413

Prime factors of 1413 are 3, 157. Prime factorization of 1413 in exponential form is:

1413 = 3² × 157¹

Step-3: Factors of 1407

List of positive integer factors of 1407 that divides 1407 without a remainder.

1, 3, 7, 21, 67, 201, 469

Step-4: Factors of 1413

List of positive integer factors of 1413 that divides 1407 without a remainder.

1, 3, 9, 157, 471

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1407 and 1413. The biggest common factor number is the GCF number.
So the greatest common factor 1407 and 1413 is 3.

Also check out the Least Common Multiple of 1407 and 1413