Highest Common Factor of 500, 825, 918 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 500, 825, 918 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 500, 825, 918 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 500, 825, 918 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 500, 825, 918 is 1.

HCF(500, 825, 918) = 1

HCF of 500, 825, 918 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 500, 825, 918 is 1.

Highest Common Factor of 500,825,918 using Euclid's algorithm

Highest Common Factor of 500,825,918 is 1

Step 1: Since 825 > 500, we apply the division lemma to 825 and 500, to get

825 = 500 x 1 + 325

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 325 and 500, to get

500 = 325 x 1 + 175

Step 3: We consider the new divisor 325 and the new remainder 175, and apply the division lemma to get

325 = 175 x 1 + 150

We consider the new divisor 175 and the new remainder 150,and apply the division lemma to get

175 = 150 x 1 + 25

We consider the new divisor 150 and the new remainder 25,and apply the division lemma to get

150 = 25 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 500 and 825 is 25

Notice that 25 = HCF(150,25) = HCF(175,150) = HCF(325,175) = HCF(500,325) = HCF(825,500) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 918 > 25, we apply the division lemma to 918 and 25, to get

918 = 25 x 36 + 18

Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 18 and 25, to get

25 = 18 x 1 + 7

Step 3: We consider the new divisor 18 and the new remainder 7, and apply the division lemma to get

18 = 7 x 2 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 25 and 918 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(25,18) = HCF(918,25) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 500, 825, 918 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 500, 825, 918?

Answer: HCF of 500, 825, 918 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 500, 825, 918 using Euclid's Algorithm?

Answer: For arbitrary numbers 500, 825, 918 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.