Greatest Common Factor of 67 and 69

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

• Greatest Common Factor of 67 and 69 by prime factorization method
• Greatest Common Factor of 67 and 69 by matching factors method

Prime Factorization of 67

Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:

67 = 67¹

Prime Factorization of 69

Prime factors of 69 are 3.Prime factorization of 69 in exponential form is:

69 = 3¹×23¹

∴ So by taking common prime factors GCF of 67 and 69 is 1

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1,67

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Greatest Common Factor

We found the factors and prime factorization of 67 and 69. The biggest common factor number is the GCF number.
So the greatest common factor 67 and 69 is 1.

Also check out the Least Common Multiple of 67 and 69

(i) The GCF of 67 and 69 is associative

GCF of 67 and 69 = GCF of 69 and 67

1. What is the GCF of 67 and 69?

Answer: GCF of 67 and 69 is 1.

2. What are the Factors of 67?

Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.

3. What are the Factors of 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

4. How to Find the GCF of 67 and 69?

Answer:

Greatest Common Factor of 67 and 69 = 1

Step 1: Find the prime factorization of 67

67 = 67

Step 2: Find the prime factorization of 69

69 = 3 x 23

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 67 and 69 is 1