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, 1408 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1406 and 1408 is 2.
GCF(1406,1408) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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 1408
2 | 1408 |
2 | 704 |
2 | 352 |
2 | 176 |
2 | 88 |
2 | 44 |
2 | 22 |
11 | 11 |
1 |
Prime factors of 1408 are 2,11. Prime factorization of 1408 in exponential form is:
1408 = 27×111
∴ So by taking common prime factors GCF of 1406 and 1408 is 2
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 1408
List of positive integer factors of 1408 that divides 1408 without a remainder.
1,2,4,8,11,16,22,32,44,64,88,128,176,352,704,1408
Greatest Common Factor
We found the factors and prime factorization of 1406 and 1408. The biggest common factor number is the GCF number.
So the greatest common factor 1406 and 1408 is 2.
Also check out the Least Common Multiple of 1406 and 1408
(i) The GCF of 1406 and 1408 is associative
GCF of 1406 and 1408 = GCF of 1408 and 1406
1. What is the GCF of 1406 and 1408?
Answer: GCF of 1406 and 1408 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 1408?
Answer: Factors of 1408 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408. There are 16 integers that are factors of 1408. The greatest factor of 1408 is 1408.
4. How to Find the GCF of 1406 and 1408?
Answer:
Greatest Common Factor of 1406 and 1408 = 2
Step 1: Find the prime factorization of 1406
1406 = 2 x 19 x 37
Step 2: Find the prime factorization of 1408
1408 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11
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 1408 is 2