Greatest Common Factor of 1406 and 1414

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 1406, 1414 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1406 and 1414 is 2.

GCF(1406,1414) = 2

GCF of 1406 and 1414

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

GCF of:
and

Greatest Common Factor of 1406 and 1414

GCF of 1406 and 1414 is 2

Prime Factorization of 1406


2 1406
19 703
37 37
1

Prime factors of 1406 are 2,19,37. Prime factorization of 1406 in exponential form is:

1406 = 21×191×371

Prime Factorization of 1414


2 1414
7 707
101 101
1

Prime factors of 1414 are 2,7,101. Prime factorization of 1414 in exponential form is:

1414 = 21×71×1011

∴ So by taking common prime factors GCF of 1406 and 1414 is 2

Greatest Common Factor of 1406 and 1414 by matching factors method

Factors of 1406

List of positive integer factors of 1406 that divides 1406 without a remainder.

1,2,19,37,38,74,703,1406

Factors of 1414

List of positive integer factors of 1414 that divides 1414 without a remainder.

1,2,7,14,101,202,707,1414

Greatest Common Factor

We found the factors and prime factorization of 1406 and 1414. The biggest common factor number is the GCF number.
So the greatest common factor 1406 and 1414 is 2.

Also check out the Least Common Multiple of 1406 and 1414

Properties of GCF 1406 and 1414

(i) The GCF of 1406 and 1414 is associative

GCF of 1406 and 1414 = GCF of 1414 and 1406

Related Greatest Common Factor of 1406

Related Greatest Common Factor of 1414

Frequently Asked Questions on GCF of 1406 and 1414

1. What is the GCF of 1406 and 1414?

Answer: GCF of 1406 and 1414 is 2.

2. What are the Factors of 1406?

Answer: Factors of 1406 are 1, 2, 19, 37, 38, 74, 703, 1406. There are 8 integers that are factors of 1406. The greatest factor of 1406 is 1406.

3. What are the Factors of 1414?

Answer: Factors of 1414 are 1, 2, 7, 14, 101, 202, 707, 1414. There are 8 integers that are factors of 1414. The greatest factor of 1414 is 1414.

4. How to Find the GCF of 1406 and 1414?

Answer:

Greatest Common Factor of 1406 and 1414 = 2

Step 1: Find the prime factorization of 1406

1406 = 2 x 19 x 37

Step 2: Find the prime factorization of 1414

1414 = 2 x 7 x 101

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

GCF = 2

Step 4: Therefore, the greatest common factor of 1406 and 1414 is 2