Greatest Common Factor of 409 and 417

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

• Greatest Common Factor of 409 and 417 by prime factorization method
• Greatest Common Factor of 409 and 417 by matching factors method

Prime Factorization of 409

Prime factors of 409 are 409. Prime factorization of 409 in exponential form is:

409 = 409¹

Prime Factorization of 417

Prime factors of 417 are 3.Prime factorization of 417 in exponential form is:

417 = 3¹×139¹

∴ So by taking common prime factors GCF of 409 and 417 is 1

Factors of 409

List of positive integer factors of 409 that divides 409 without a remainder.

1,409

Factors of 417

List of positive integer factors of 417 that divides 417 without a remainder.

1,3,139,417

Greatest Common Factor

We found the factors and prime factorization of 409 and 417. The biggest common factor number is the GCF number.
So the greatest common factor 409 and 417 is 1.

Also check out the Least Common Multiple of 409 and 417

(i) The GCF of 409 and 417 is associative

GCF of 409 and 417 = GCF of 417 and 409

1. What is the GCF of 409 and 417?

Answer: GCF of 409 and 417 is 1.

2. What are the Factors of 409?

Answer: Factors of 409 are 1, 409. There are 2 integers that are factors of 409. The greatest factor of 409 is 409.

3. What are the Factors of 417?

Answer: Factors of 417 are 1, 3, 139, 417. There are 4 integers that are factors of 417. The greatest factor of 417 is 417.

4. How to Find the GCF of 409 and 417?

Answer:

Greatest Common Factor of 409 and 417 = 1

Step 1: Find the prime factorization of 409

409 = 409

Step 2: Find the prime factorization of 417

417 = 3 x 139

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 409 and 417 is 1