Greatest Common Factor of 398 and 406

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 398, 406 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 398 and 406 is 2.

GCF(398,406) = 2

GCF of 398 and 406

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

GCF of:
and

Greatest Common Factor of 398 and 406

GCF of 398 and 406 is 2

Prime Factorization of 398


2 398
199 199
1

Prime factors of 398 are 2,199. Prime factorization of 398 in exponential form is:

398 = 21×1991

Prime Factorization of 406


2 406
7 203
29 29
1

Prime factors of 406 are 2,7,29. Prime factorization of 406 in exponential form is:

406 = 21×71×291

∴ So by taking common prime factors GCF of 398 and 406 is 2

Greatest Common Factor of 398 and 406 by matching factors method

Factors of 398

List of positive integer factors of 398 that divides 398 without a remainder.

1,2,199,398

Factors of 406

List of positive integer factors of 406 that divides 406 without a remainder.

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors and prime factorization of 398 and 406. The biggest common factor number is the GCF number.
So the greatest common factor 398 and 406 is 2.

Also check out the Least Common Multiple of 398 and 406

Properties of GCF 398 and 406

(i) The GCF of 398 and 406 is associative

GCF of 398 and 406 = GCF of 406 and 398

Related Greatest Common Factor of 398

Related Greatest Common Factor of 406

Frequently Asked Questions on GCF of 398 and 406

1. What is the GCF of 398 and 406?

Answer: GCF of 398 and 406 is 2.

2. What are the Factors of 398?

Answer: Factors of 398 are 1, 2, 199, 398. There are 4 integers that are factors of 398. The greatest factor of 398 is 398.

3. What are the Factors of 406?

Answer: Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406. There are 8 integers that are factors of 406. The greatest factor of 406 is 406.

4. How to Find the GCF of 398 and 406?

Answer:

Greatest Common Factor of 398 and 406 = 2

Step 1: Find the prime factorization of 398

398 = 2 x 199

Step 2: Find the prime factorization of 406

406 = 2 x 7 x 29

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 398 and 406 is 2