Greatest Common Factor of 67 and 74

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

• Greatest Common Factor of 67 and 74 by prime factorization method
• Greatest Common Factor of 67 and 74 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 74

Prime factors of 74 are 2.Prime factorization of 74 in exponential form is:

74 = 2¹×37¹

∴ So by taking common prime factors GCF of 67 and 74 is 1

Factors of 67

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

1,67

Factors of 74

List of positive integer factors of 74 that divides 74 without a remainder.

1,2,37,74

Greatest Common Factor

We found the factors and prime factorization of 67 and 74. The biggest common factor number is the GCF number.
So the greatest common factor 67 and 74 is 1.

Also check out the Least Common Multiple of 67 and 74

(i) The GCF of 67 and 74 is associative

GCF of 67 and 74 = GCF of 74 and 67

1. What is the GCF of 67 and 74?

Answer: GCF of 67 and 74 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 74?

Answer: Factors of 74 are 1, 2, 37, 74. There are 4 integers that are factors of 74. The greatest factor of 74 is 74.

4. How to Find the GCF of 67 and 74?

Answer:

Greatest Common Factor of 67 and 74 = 1

Step 1: Find the prime factorization of 67

67 = 67

Step 2: Find the prime factorization of 74

74 = 2 x 37

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 74 is 1