Highest Common Factor of 403, 971, 706 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 403, 971, 706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 403, 971, 706 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 403, 971, 706 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 403, 971, 706 is 1.

HCF(403, 971, 706) = 1

HCF of 403, 971, 706 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 403, 971, 706 is 1.

Highest Common Factor of 403,971,706 using Euclid's algorithm

Highest Common Factor of 403,971,706 is 1

Step 1: Since 971 > 403, we apply the division lemma to 971 and 403, to get

971 = 403 x 2 + 165

Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 165 and 403, to get

403 = 165 x 2 + 73

Step 3: We consider the new divisor 165 and the new remainder 73, and apply the division lemma to get

165 = 73 x 2 + 19

We consider the new divisor 73 and the new remainder 19,and apply the division lemma to get

73 = 19 x 3 + 16

We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get

19 = 16 x 1 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 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 403 and 971 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(73,19) = HCF(165,73) = HCF(403,165) = HCF(971,403) .

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

Step 1: Since 706 > 1, we apply the division lemma to 706 and 1, to get

706 = 1 x 706 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 706 is 1

Notice that 1 = HCF(706,1) .

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Frequently Asked Questions on HCF of 403, 971, 706 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 403, 971, 706?

Answer: HCF of 403, 971, 706 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 403, 971, 706 using Euclid's Algorithm?

Answer: For arbitrary numbers 403, 971, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.