Greatest Common Factor of 1414 and 1420

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 1414, 1420 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1414 and 1420 is 2.

GCF(1414,1420) = 2

GCF of 1414 and 1420

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

GCF of:
and

Greatest Common Factor of 1414 and 1420

GCF of 1414 and 1420 is 2

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

Prime Factorization of 1420


2 1420
2 710
5 355
71 71
1

Prime factors of 1420 are 2,5,71. Prime factorization of 1420 in exponential form is:

1420 = 22×51×711

∴ So by taking common prime factors GCF of 1414 and 1420 is 2

Greatest Common Factor of 1414 and 1420 by matching factors method

Factors of 1414

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

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

Factors of 1420

List of positive integer factors of 1420 that divides 1420 without a remainder.

1,2,4,5,10,20,71,142,284,355,710,1420

Greatest Common Factor

We found the factors and prime factorization of 1414 and 1420. The biggest common factor number is the GCF number.
So the greatest common factor 1414 and 1420 is 2.

Also check out the Least Common Multiple of 1414 and 1420

Properties of GCF 1414 and 1420

(i) The GCF of 1414 and 1420 is associative

GCF of 1414 and 1420 = GCF of 1420 and 1414

Related Greatest Common Factor of 1414

Related Greatest Common Factor of 1420

Frequently Asked Questions on GCF of 1414 and 1420

1. What is the GCF of 1414 and 1420?

Answer: GCF of 1414 and 1420 is 2.

2. 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.

3. What are the Factors of 1420?

Answer: Factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420. There are 12 integers that are factors of 1420. The greatest factor of 1420 is 1420.

4. How to Find the GCF of 1414 and 1420?

Answer:

Greatest Common Factor of 1414 and 1420 = 2

Step 1: Find the prime factorization of 1414

1414 = 2 x 7 x 101

Step 2: Find the prime factorization of 1420

1420 = 2 x 2 x 5 x 71

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 1414 and 1420 is 2