Highest Common Factor of 685, 472, 117 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 685, 472, 117 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 472, 117 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 685, 472, 117 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 685, 472, 117 is 1.

HCF(685, 472, 117) = 1

HCF of 685, 472, 117 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 685, 472, 117 is 1.

Highest Common Factor of 685,472,117 using Euclid's algorithm

Highest Common Factor of 685,472,117 is 1

Step 1: Since 685 > 472, we apply the division lemma to 685 and 472, to get

685 = 472 x 1 + 213

Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 213 and 472, to get

472 = 213 x 2 + 46

Step 3: We consider the new divisor 213 and the new remainder 46, and apply the division lemma to get

213 = 46 x 4 + 29

We consider the new divisor 46 and the new remainder 29,and apply the division lemma to get

46 = 29 x 1 + 17

We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get

29 = 17 x 1 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 685 and 472 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(46,29) = HCF(213,46) = HCF(472,213) = HCF(685,472) .

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

Step 1: Since 117 > 1, we apply the division lemma to 117 and 1, to get

117 = 1 x 117 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 117 is 1

Notice that 1 = HCF(117,1) .

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Frequently Asked Questions on HCF of 685, 472, 117 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 685, 472, 117?

Answer: HCF of 685, 472, 117 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 472, 117 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 472, 117 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.