Highest Common Factor of 682, 890, 159 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 682, 890, 159 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 682, 890, 159 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 682, 890, 159 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 682, 890, 159 is 1.

HCF(682, 890, 159) = 1

HCF of 682, 890, 159 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 682, 890, 159 is 1.

Highest Common Factor of 682,890,159 using Euclid's algorithm

Highest Common Factor of 682,890,159 is 1

Step 1: Since 890 > 682, we apply the division lemma to 890 and 682, to get

890 = 682 x 1 + 208

Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 208 and 682, to get

682 = 208 x 3 + 58

Step 3: We consider the new divisor 208 and the new remainder 58, and apply the division lemma to get

208 = 58 x 3 + 34

We consider the new divisor 58 and the new remainder 34,and apply the division lemma to get

58 = 34 x 1 + 24

We consider the new divisor 34 and the new remainder 24,and apply the division lemma to get

34 = 24 x 1 + 10

We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get

24 = 10 x 2 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 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 682 and 890 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(34,24) = HCF(58,34) = HCF(208,58) = HCF(682,208) = HCF(890,682) .

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

Step 1: Since 159 > 2, we apply the division lemma to 159 and 2, to get

159 = 2 x 79 + 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 159 is 1

Notice that 1 = HCF(2,1) = HCF(159,2) .

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Frequently Asked Questions on HCF of 682, 890, 159 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 682, 890, 159?

Answer: HCF of 682, 890, 159 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 682, 890, 159 using Euclid's Algorithm?

Answer: For arbitrary numbers 682, 890, 159 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.