GCD of 675, 420, 105 Calculator
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Online GCD Calculator is useful to find the GCD of 675, 420, 105 quickly. Get the easiest ways to solve the greatest common divisor of 675, 420, 105 i.e 15 in different methods as follows.
Given Input numbers are 675, 420, 105
In the factoring method, we have to find the divisors of all numbers
Divisors of 675 :
The positive integer divisors of 675 that completely divides 675 are.
1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
Divisors of 420 :
The positive integer divisors of 420 that completely divides 420 are.
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
Divisors of 105 :
The positive integer divisors of 105 that completely divides 105 are.
1, 3, 5, 7, 15, 21, 35, 105
GCD of numbers is the greatest common divisor
So, the GCD (675, 420, 105) = 15.
Given numbers are 675, 420, 105
The list of prime factors of all numbers are
Prime factors of 675 are 3 x 3 x 3 x 5 x 5
Prime factors of 420 are 2 x 2 x 3 x 5 x 7
Prime factors of 105 are 3 x 5 x 7
The highest common occurrence is 31 x 51
Therefore, GCD of 675, 420, 105 is 15.
Steps to Calculate GCD of 675, 420, 105 using LCM Formula
Given numbers are 675, 420, 105
GCD of 2 numbers formula is GCD(a, b) = ( a x b) / LCM(a, b)
Apply this formula for all numbers.
Step1:
LCM(675, 420) = 18900
GCD(675, 420) = ( 675 x 420 ) / 18900
= 675 / 420
= 675
Step2:
LCM(15, 105) = 105
GCD(15, 105) = ( 15 x 105 ) / 105
= 15 / 105
= 15
So, Greatest Common Divisor of 675, 420, 105 is 15
GCD of Numbers Calculation Examples
Here are some samples of GCD of Numbers calculations.
Greatest Common Divisor of 675, 420, 105
Given numbers are 675, 420, 105
The greatest common divisor of numbers 675, 420, 105 can be found in various methods such as the LCM formula, factoring, and prime factorization. The GCD of numbers 675, 420, 105 is 15.
FAQs on GCD of 675, 420, 105 Calculator
1. What is the GCD of 675, 420, 105?
GCD of given numbers 675, 420, 105 is 15
2. How to calculate the greatest common divisor of 675, 420, 105?
We can find the highest common divisor of 675, 420, 105 easily using the prime factorization method. Just list the prime factors of all numbers and pick the highest common factor which is the GCD of 675, 420, 105 i.e 15.
3. How can I use the GCD of 675, 420, 105Calculator?
Out the numbers 675, 420, 105 into the GCD calculator and hit the calculate button to get the greatest common divisor as result.