Highest Common Factor of 661, 474, 236 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 661, 474, 236 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 661, 474, 236 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 661, 474, 236 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 661, 474, 236 is 1.

HCF(661, 474, 236) = 1

HCF of 661, 474, 236 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 661, 474, 236 is 1.

Highest Common Factor of 661,474,236 using Euclid's algorithm

Highest Common Factor of 661,474,236 is 1

Step 1: Since 661 > 474, we apply the division lemma to 661 and 474, to get

661 = 474 x 1 + 187

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 187 and 474, to get

474 = 187 x 2 + 100

Step 3: We consider the new divisor 187 and the new remainder 100, and apply the division lemma to get

187 = 100 x 1 + 87

We consider the new divisor 100 and the new remainder 87,and apply the division lemma to get

100 = 87 x 1 + 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 661 and 474 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(87,13) = HCF(100,87) = HCF(187,100) = HCF(474,187) = HCF(661,474) .

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

Step 1: Since 236 > 1, we apply the division lemma to 236 and 1, to get

236 = 1 x 236 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 236 is 1

Notice that 1 = HCF(236,1) .

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Frequently Asked Questions on HCF of 661, 474, 236 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 661, 474, 236?

Answer: HCF of 661, 474, 236 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 661, 474, 236 using Euclid's Algorithm?

Answer: For arbitrary numbers 661, 474, 236 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.