What is the Greatest Common Factor of 810 and 825?
Greatest common factor (GCF) of 810 and 825 is 15.
GCF(810,825) = 15
We will now calculate the prime factors of 810 and 825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 810 and 825.
How to find the GCF of 810 and 825?
We will first find the prime factorization of 810 and 825. After we will calculate the factors of 810 and 825 and find the biggest common factor number .
Step-1: Prime Factorization of 810
Prime factors of 810 are 2, 3, 5. Prime factorization of 810 in exponential form is:
810 = 21 × 34 × 51
Step-2: Prime Factorization of 825
Prime factors of 825 are 3, 5, 11. Prime factorization of 825 in exponential form is:
825 = 31 × 52 × 111
Step-3: Factors of 810
List of positive integer factors of 810 that divides 810 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405
Step-4: Factors of 825
List of positive integer factors of 825 that divides 810 without a remainder.
1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 810 and 825. The biggest common factor number is the GCF number.
So the greatest common factor 810 and 825 is 15.
Also check out the Least Common Multiple of 810 and 825
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