Greatest Common Factor of 67000 and 67002

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 67000, 67002 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 67000 and 67002 is 2.

GCF(67000,67002) = 2

GCF of 67000 and 67002

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

GCF of:
and

Greatest Common Factor of 67000 and 67002

GCF of 67000 and 67002 is 2

Prime Factorization of 67000


2 67000
2 33500
2 16750
5 8375
5 1675
5 335
67 67
1

Prime factors of 67000 are 2,5,67. Prime factorization of 67000 in exponential form is:

67000 = 23×53×671

Prime Factorization of 67002


2 67002
3 33501
13 11167
859 859
1

Prime factors of 67002 are 2,3,13,859. Prime factorization of 67002 in exponential form is:

67002 = 21×31×131×8591

∴ So by taking common prime factors GCF of 67000 and 67002 is 2

Greatest Common Factor of 67000 and 67002 by matching factors method

Factors of 67000

List of positive integer factors of 67000 that divides 67000 without a remainder.

1,2,4,5,8,10,20,25,40,50,67,100,125,134,200,250,268,335,500,536,670,1000,1340,1675,2680,3350,6700,8375,13400,16750,33500,67000

Factors of 67002

List of positive integer factors of 67002 that divides 67002 without a remainder.

1,2,3,6,13,26,39,78,859,1718,2577,5154,11167,22334,33501,67002

Greatest Common Factor

We found the factors and prime factorization of 67000 and 67002. The biggest common factor number is the GCF number.
So the greatest common factor 67000 and 67002 is 2.

Also check out the Least Common Multiple of 67000 and 67002

Properties of GCF 67000 and 67002

(i) The GCF of 67000 and 67002 is associative

GCF of 67000 and 67002 = GCF of 67002 and 67000

Related Greatest Common Factor of 67000

Related Greatest Common Factor of 67002

Frequently Asked Questions on GCF of 67000 and 67002

1. What is the GCF of 67000 and 67002?

Answer: GCF of 67000 and 67002 is 2.

2. What are the Factors of 67000?

Answer: Factors of 67000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 125, 134, 200, 250, 268, 335, 500, 536, 670, 1000, 1340, 1675, 2680, 3350, 6700, 8375, 13400, 16750, 33500, 67000. There are 32 integers that are factors of 67000. The greatest factor of 67000 is 67000.

3. What are the Factors of 67002?

Answer: Factors of 67002 are 1, 2, 3, 6, 13, 26, 39, 78, 859, 1718, 2577, 5154, 11167, 22334, 33501, 67002. There are 16 integers that are factors of 67002. The greatest factor of 67002 is 67002.

4. How to Find the GCF of 67000 and 67002?

Answer:

Greatest Common Factor of 67000 and 67002 = 2

Step 1: Find the prime factorization of 67000

67000 = 2 x 2 x 2 x 5 x 5 x 5 x 67

Step 2: Find the prime factorization of 67002

67002 = 2 x 3 x 13 x 859

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 67000 and 67002 is 2