Highest Common Factor of 680, 178, 135 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 680, 178, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 680, 178, 135 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 680, 178, 135 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 680, 178, 135 is 1.

HCF(680, 178, 135) = 1

HCF of 680, 178, 135 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 680, 178, 135 is 1.

Highest Common Factor of 680,178,135 using Euclid's algorithm

Highest Common Factor of 680,178,135 is 1

Step 1: Since 680 > 178, we apply the division lemma to 680 and 178, to get

680 = 178 x 3 + 146

Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 146 and 178, to get

178 = 146 x 1 + 32

Step 3: We consider the new divisor 146 and the new remainder 32, and apply the division lemma to get

146 = 32 x 4 + 18

We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get

32 = 18 x 1 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 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 680 and 178 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(146,32) = HCF(178,146) = HCF(680,178) .

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

Step 1: Since 135 > 2, we apply the division lemma to 135 and 2, to get

135 = 2 x 67 + 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 135 is 1

Notice that 1 = HCF(2,1) = HCF(135,2) .

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Frequently Asked Questions on HCF of 680, 178, 135 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 680, 178, 135?

Answer: HCF of 680, 178, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 680, 178, 135 using Euclid's Algorithm?

Answer: For arbitrary numbers 680, 178, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.