Highest Common Factor of 455, 169, 971 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 455, 169, 971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 455, 169, 971 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 455, 169, 971 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 455, 169, 971 is 1.

HCF(455, 169, 971) = 1

HCF of 455, 169, 971 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 455, 169, 971 is 1.

Highest Common Factor of 455,169,971 using Euclid's algorithm

Highest Common Factor of 455,169,971 is 1

Step 1: Since 455 > 169, we apply the division lemma to 455 and 169, to get

455 = 169 x 2 + 117

Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 117 and 169, to get

169 = 117 x 1 + 52

Step 3: We consider the new divisor 117 and the new remainder 52, and apply the division lemma to get

117 = 52 x 2 + 13

We consider the new divisor 52 and the new remainder 13, and apply the division lemma to get

52 = 13 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 455 and 169 is 13

Notice that 13 = HCF(52,13) = HCF(117,52) = HCF(169,117) = HCF(455,169) .

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

Step 1: Since 971 > 13, we apply the division lemma to 971 and 13, to get

971 = 13 x 74 + 9

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 9 and 13, to get

13 = 9 x 1 + 4

Step 3: We consider the new divisor 9 and the new remainder 4, and apply the division lemma to get

9 = 4 x 2 + 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 13 and 971 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(971,13) .

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Frequently Asked Questions on HCF of 455, 169, 971 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 455, 169, 971?

Answer: HCF of 455, 169, 971 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 455, 169, 971 using Euclid's Algorithm?

Answer: For arbitrary numbers 455, 169, 971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.