Highest Common Factor of 650, 2117 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 650, 2117 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 650, 2117 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 650, 2117 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 650, 2117 is 1.

HCF(650, 2117) = 1

HCF of 650, 2117 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 650, 2117 is 1.

Highest Common Factor of 650,2117 using Euclid's algorithm

Highest Common Factor of 650,2117 is 1

Step 1: Since 2117 > 650, we apply the division lemma to 2117 and 650, to get

2117 = 650 x 3 + 167

Step 2: Since the reminder 650 ≠ 0, we apply division lemma to 167 and 650, to get

650 = 167 x 3 + 149

Step 3: We consider the new divisor 167 and the new remainder 149, and apply the division lemma to get

167 = 149 x 1 + 18

We consider the new divisor 149 and the new remainder 18,and apply the division lemma to get

149 = 18 x 8 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 650 and 2117 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(149,18) = HCF(167,149) = HCF(650,167) = HCF(2117,650) .

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Frequently Asked Questions on HCF of 650, 2117 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 650, 2117?

Answer: HCF of 650, 2117 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 650, 2117 using Euclid's Algorithm?

Answer: For arbitrary numbers 650, 2117 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.