Greatest Common Factor of 1700 and 1705

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 1700, 1705 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1700 and 1705 is 5.

GCF(1700,1705) = 5

GCF of 1700 and 1705

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

GCF of:
and

Greatest Common Factor of 1700 and 1705

GCF of 1700 and 1705 is 5

Prime Factorization of 1700


2 1700
2 850
5 425
5 85
17 17
1

Prime factors of 1700 are 2,5,17. Prime factorization of 1700 in exponential form is:

1700 = 22×52×171

Prime Factorization of 1705


5 1705
11 341
31 31
1

Prime factors of 1705 are 5,11,31. Prime factorization of 1705 in exponential form is:

1705 = 51×111×311

∴ So by taking common prime factors GCF of 1700 and 1705 is 5

Greatest Common Factor of 1700 and 1705 by matching factors method

Factors of 1700

List of positive integer factors of 1700 that divides 1700 without a remainder.

1,2,4,5,10,17,20,25,34,50,68,85,100,170,340,425,850,1700

Factors of 1705

List of positive integer factors of 1705 that divides 1705 without a remainder.

1,5,11,31,55,155,341,1705

Greatest Common Factor

We found the factors and prime factorization of 1700 and 1705. The biggest common factor number is the GCF number.
So the greatest common factor 1700 and 1705 is 5.

Also check out the Least Common Multiple of 1700 and 1705

Properties of GCF 1700 and 1705

(i) The GCF of 1700 and 1705 is associative

GCF of 1700 and 1705 = GCF of 1705 and 1700

Related Greatest Common Factor of 1700

Related Greatest Common Factor of 1705

Frequently Asked Questions on GCF of 1700 and 1705

1. What is the GCF of 1700 and 1705?

Answer: GCF of 1700 and 1705 is 5.

2. What are the Factors of 1700?

Answer: Factors of 1700 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700. There are 18 integers that are factors of 1700. The greatest factor of 1700 is 1700.

3. What are the Factors of 1705?

Answer: Factors of 1705 are 1, 5, 11, 31, 55, 155, 341, 1705. There are 8 integers that are factors of 1705. The greatest factor of 1705 is 1705.

4. How to Find the GCF of 1700 and 1705?

Answer:

Greatest Common Factor of 1700 and 1705 = 5

Step 1: Find the prime factorization of 1700

1700 = 2 x 2 x 5 x 5 x 17

Step 2: Find the prime factorization of 1705

1705 = 5 x 11 x 31

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

GCF = 5

Step 4: Therefore, the greatest common factor of 1700 and 1705 is 5