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How to Find the GCF Using Euclid’s Algorithm

Calculator Use

Calculate GCF, GCD, and HCF of a fixed of or greater numbers and notice the paintings the usage of factorization.

Enter 2 or greater entire numbers separated with the aid of using commas or spaces.

The Greatest Common Factor Calculator answer additionally works as an answer for locating:

  • Greatest not unusual place element (GCF)
  • Greatest not unusual place denominator (GCD)
  • Highest not unusual place element (HCF)
  • Greatest not unusual place divisor (GCD)

How to Find the GCF Using Euclid’s Algorithm

  1. Given entire numbers, subtract the smaller quantity from the bigger quantity and notice the end result.
  2. Repeat the system subtracting the smaller quantity from the end result till the end result is smaller than the authentic small quantity.
  3. Use the authentic small quantity as the brand new large quantity. Subtract the end result from Step 2 from the brand new large quantity.
  4. Repeat the system for each new large quantity and smaller quantity till you attain 0.
  5. When you attain 0, cross again one calculation: the GCF is the quantity you determined simply earlier than the 0 end result.

For extra data see our Euclid’s Algorithm Calculator.

https://gcfcalculator.net/

Example: Find the GCF (18, 27)

27 – 18 = 9

18 – 9 – 9 = zero

So, the finest not unusual place element of 18 and 27 is 9, the smallest end result we had earlier than we reached zero.

Example: Find the GCF (20, 50, one hundred twenty)

Note that the GCF (x,y,z) = GCF (GCF (x,y),z). In different words, the GCF of three or greater numbers may be determined with the aid of using locating the GCF of two numbers and the usage of the end result together with the subsequent quantity to locate the GCF and so on.

Let’s get the GCF (one hundred twenty,50) first

one hundred twenty – 50 – 50 = one hundred twenty – (50 * 2) = 20

50 – 20 – 20 = 50 – (20 * 2) = 10

20 – 10 – 10 = 20 – (10 * 2) = zero

So, the finest not un usual place element of one hundred twenty and 50 is 10.

Now let’s locate the GCF of our 1/3 value, 20, and our end result, 10. GCF (20,10)

20 – 10 – 10 = 20 – (10 * 2) = zero

So, the finest not un usual place element of 20 and 10 is 10.

Therefore, the finest not unusual place element of one hundred twenty, 50 and 20 is 10.

Example: Find the GCF (182664, 154875, 137688) or GCF (GCF(182664, 154875), 137688)

First we discover the GCF (182664, 154875)

182664 – (154875 * 1) = 27789

154875 – (27789 * five) = 15930

27789 – (15930 * 1) = 11859

15930 – (11859 * 1) = 4071

11859 – (4071 * 2) = 3717

4071 – (3717 * 1) = 354

3717 – (354 * 10) = 177

354 – (177 * 2) = zero

So, the the finest not un usual place element of 182664 and 154875 is 177.

Now we discover the GCF (177, 137688)

137688 – (177 * 777) = 159

177 – (159 * 1) = 18

159 – (18 * 8) = 15

18 – (15 * 1) = three

15 – (three * five) = zero

So, the finest not un usual place element of 177 and 137688 is three.

Therefore, the finest not Lcm calculator place element of 182664, 154875 and 137688 is three.

 

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