Highest Common Factor of 274, 461, 140 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 274, 461, 140 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 274, 461, 140 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 274, 461, 140 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 274, 461, 140 is 1.

HCF(274, 461, 140) = 1

HCF of 274, 461, 140 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 274, 461, 140 is 1.

Highest Common Factor of 274,461,140 using Euclid's algorithm

Highest Common Factor of 274,461,140 is 1

Step 1: Since 461 > 274, we apply the division lemma to 461 and 274, to get

461 = 274 x 1 + 187

Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 187 and 274, to get

274 = 187 x 1 + 87

Step 3: We consider the new divisor 187 and the new remainder 87, and apply the division lemma to get

187 = 87 x 2 + 13

We consider the new divisor 87 and the new remainder 13,and apply the division lemma to get

87 = 13 x 6 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

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 274 and 461 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(87,13) = HCF(187,87) = HCF(274,187) = HCF(461,274) .

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

Step 1: Since 140 > 1, we apply the division lemma to 140 and 1, to get

140 = 1 x 140 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 140 is 1

Notice that 1 = HCF(140,1) .

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Frequently Asked Questions on HCF of 274, 461, 140 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 274, 461, 140?

Answer: HCF of 274, 461, 140 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 274, 461, 140 using Euclid's Algorithm?

Answer: For arbitrary numbers 274, 461, 140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.