What is the Greatest Common Factor of 36409 and 36414?

Greatest common factor (GCF) of 36409 and 36414 is 1.

GCF(36409,36414) = 1

We will now calculate the prime factors of 36409 and 36414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36409 and 36414.

How to find the GCF of 36409 and 36414?

We will first find the prime factorization of 36409 and 36414. After we will calculate the factors of 36409 and 36414 and find the biggest common factor number .

Step-1: Prime Factorization of 36409

Prime factors of 36409 are 23, 1583. Prime factorization of 36409 in exponential form is:

36409 = 23¹ × 1583¹

Step-2: Prime Factorization of 36414

Prime factors of 36414 are 2, 3, 7, 17. Prime factorization of 36414 in exponential form is:

36414 = 2¹ × 3² × 7¹ × 17²

Step-3: Factors of 36409

List of positive integer factors of 36409 that divides 36409 without a remainder.

1, 23, 1583

Step-4: Factors of 36414

List of positive integer factors of 36414 that divides 36409 without a remainder.

1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 289, 306, 357, 578, 714, 867, 1071, 1734, 2023, 2142, 2601, 4046, 5202, 6069, 12138, 18207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36409 and 36414. The biggest common factor number is the GCF number.
So the greatest common factor 36409 and 36414 is 1.

Also check out the Least Common Multiple of 36409 and 36414