Highest Common Factor of 410, 746, 917 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 410, 746, 917 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 410, 746, 917 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 410, 746, 917 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 410, 746, 917 is 1.

HCF(410, 746, 917) = 1

HCF of 410, 746, 917 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 410, 746, 917 is 1.

Highest Common Factor of 410,746,917 using Euclid's algorithm

Highest Common Factor of 410,746,917 is 1

Step 1: Since 746 > 410, we apply the division lemma to 746 and 410, to get

746 = 410 x 1 + 336

Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 336 and 410, to get

410 = 336 x 1 + 74

Step 3: We consider the new divisor 336 and the new remainder 74, and apply the division lemma to get

336 = 74 x 4 + 40

We consider the new divisor 74 and the new remainder 40,and apply the division lemma to get

74 = 40 x 1 + 34

We consider the new divisor 40 and the new remainder 34,and apply the division lemma to get

40 = 34 x 1 + 6

We consider the new divisor 34 and the new remainder 6,and apply the division lemma to get

34 = 6 x 5 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 410 and 746 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) = HCF(40,34) = HCF(74,40) = HCF(336,74) = HCF(410,336) = HCF(746,410) .

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

Step 1: Since 917 > 2, we apply the division lemma to 917 and 2, to get

917 = 2 x 458 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 917 is 1

Notice that 1 = HCF(2,1) = HCF(917,2) .

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Frequently Asked Questions on HCF of 410, 746, 917 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 410, 746, 917?

Answer: HCF of 410, 746, 917 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 410, 746, 917 using Euclid's Algorithm?

Answer: For arbitrary numbers 410, 746, 917 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.