Highest Common Factor of 917, 663, 407 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 917, 663, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 917, 663, 407 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 917, 663, 407 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 917, 663, 407 is 1.

HCF(917, 663, 407) = 1

HCF of 917, 663, 407 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 917, 663, 407 is 1.

Highest Common Factor of 917,663,407 using Euclid's algorithm

Highest Common Factor of 917,663,407 is 1

Step 1: Since 917 > 663, we apply the division lemma to 917 and 663, to get

917 = 663 x 1 + 254

Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 254 and 663, to get

663 = 254 x 2 + 155

Step 3: We consider the new divisor 254 and the new remainder 155, and apply the division lemma to get

254 = 155 x 1 + 99

We consider the new divisor 155 and the new remainder 99,and apply the division lemma to get

155 = 99 x 1 + 56

We consider the new divisor 99 and the new remainder 56,and apply the division lemma to get

99 = 56 x 1 + 43

We consider the new divisor 56 and the new remainder 43,and apply the division lemma to get

56 = 43 x 1 + 13

We consider the new divisor 43 and the new remainder 13,and apply the division lemma to get

43 = 13 x 3 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 917 and 663 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(43,13) = HCF(56,43) = HCF(99,56) = HCF(155,99) = HCF(254,155) = HCF(663,254) = HCF(917,663) .

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

Step 1: Since 407 > 1, we apply the division lemma to 407 and 1, to get

407 = 1 x 407 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 407 is 1

Notice that 1 = HCF(407,1) .

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Frequently Asked Questions on HCF of 917, 663, 407 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 917, 663, 407?

Answer: HCF of 917, 663, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 917, 663, 407 using Euclid's Algorithm?

Answer: For arbitrary numbers 917, 663, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.