What is the Greatest Common Factor of 46000 and 46009?

Greatest common factor (GCF) of 46000 and 46009 is 1.

GCF(46000,46009) = 1

We will now calculate the prime factors of 46000 and 46009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 46000 and 46009.

How to find the GCF of 46000 and 46009?

We will first find the prime factorization of 46000 and 46009. After we will calculate the factors of 46000 and 46009 and find the biggest common factor number .

Step-1: Prime Factorization of 46000

Prime factors of 46000 are 2, 5, 23. Prime factorization of 46000 in exponential form is:

46000 = 2⁴ × 5³ × 23¹

Step-2: Prime Factorization of 46009

Prime factors of 46009 are 139, 331. Prime factorization of 46009 in exponential form is:

46009 = 139¹ × 331¹

Step-3: Factors of 46000

List of positive integer factors of 46000 that divides 46000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 40, 46, 50, 80, 92, 100, 115, 125, 184, 200, 230, 250, 368, 400, 460, 500, 575, 920, 1000, 1150, 1840, 2000, 2300, 2875, 4600, 5750, 9200, 11500, 23000

Step-4: Factors of 46009

List of positive integer factors of 46009 that divides 46000 without a remainder.

1, 139, 331

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 46000 and 46009. The biggest common factor number is the GCF number.
So the greatest common factor 46000 and 46009 is 1.

Also check out the Least Common Multiple of 46000 and 46009