Highest Common Factor of 868, 558, 167 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 868, 558, 167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 868, 558, 167 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 868, 558, 167 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 868, 558, 167 is 1.

HCF(868, 558, 167) = 1

HCF of 868, 558, 167 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 868, 558, 167 is 1.

Highest Common Factor of 868,558,167 using Euclid's algorithm

Highest Common Factor of 868,558,167 is 1

Step 1: Since 868 > 558, we apply the division lemma to 868 and 558, to get

868 = 558 x 1 + 310

Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 310 and 558, to get

558 = 310 x 1 + 248

Step 3: We consider the new divisor 310 and the new remainder 248, and apply the division lemma to get

310 = 248 x 1 + 62

We consider the new divisor 248 and the new remainder 62, and apply the division lemma to get

248 = 62 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 62, the HCF of 868 and 558 is 62

Notice that 62 = HCF(248,62) = HCF(310,248) = HCF(558,310) = HCF(868,558) .

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

Step 1: Since 167 > 62, we apply the division lemma to 167 and 62, to get

167 = 62 x 2 + 43

Step 2: Since the reminder 62 ≠ 0, we apply division lemma to 43 and 62, to get

62 = 43 x 1 + 19

Step 3: We consider the new divisor 43 and the new remainder 19, and apply the division lemma to get

43 = 19 x 2 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 62 and 167 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(43,19) = HCF(62,43) = HCF(167,62) .

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Frequently Asked Questions on HCF of 868, 558, 167 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 868, 558, 167?

Answer: HCF of 868, 558, 167 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 868, 558, 167 using Euclid's Algorithm?

Answer: For arbitrary numbers 868, 558, 167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.