Greatest Common Factor of 1407 and 1413

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1407, 1413 i.e. 3 largest integer by which both the numbers can be divided.

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

GCF(1407,1413) = 3

GCF of 1407 and 1413

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 1407 and 1413

GCF of 1407 and 1413 is 3

Prime Factorization of 1407


3 1407
7 469
67 67
1

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

1407 = 31×71×671

Prime Factorization of 1413


3 1413
3 471
157 157
1

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

1413 = 32×1571

∴ So by taking common prime factors GCF of 1407 and 1413 is 3

Greatest Common Factor of 1407 and 1413 by matching factors method

Factors of 1407

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

1,3,7,21,67,201,469,1407

Factors of 1413

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

1,3,9,157,471,1413

Greatest Common Factor

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

Properties of GCF 1407 and 1413

(i) The GCF of 1407 and 1413 is associative

GCF of 1407 and 1413 = GCF of 1413 and 1407

Related Greatest Common Factor of 1407

Related Greatest Common Factor of 1413

Frequently Asked Questions on GCF of 1407 and 1413

1. What is the GCF of 1407 and 1413?

Answer: GCF of 1407 and 1413 is 3.

2. What are the Factors of 1407?

Answer: Factors of 1407 are 1, 3, 7, 21, 67, 201, 469, 1407. There are 8 integers that are factors of 1407. The greatest factor of 1407 is 1407.

3. What are the Factors of 1413?

Answer: Factors of 1413 are 1, 3, 9, 157, 471, 1413. There are 6 integers that are factors of 1413. The greatest factor of 1413 is 1413.

4. How to Find the GCF of 1407 and 1413?

Answer:

Greatest Common Factor of 1407 and 1413 = 3

Step 1: Find the prime factorization of 1407

1407 = 3 x 7 x 67

Step 2: Find the prime factorization of 1413

1413 = 3 x 3 x 157

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 1407 and 1413 is 3