Highest Common Factor of 334, 661 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 334, 661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 334, 661 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 334, 661 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 334, 661 is 1.

HCF(334, 661) = 1

HCF of 334, 661 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 334, 661 is 1.

Highest Common Factor of 334,661 using Euclid's algorithm

Highest Common Factor of 334,661 is 1

Step 1: Since 661 > 334, we apply the division lemma to 661 and 334, to get

661 = 334 x 1 + 327

Step 2: Since the reminder 334 ≠ 0, we apply division lemma to 327 and 334, to get

334 = 327 x 1 + 7

Step 3: We consider the new divisor 327 and the new remainder 7, and apply the division lemma to get

327 = 7 x 46 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 334 and 661 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(327,7) = HCF(334,327) = HCF(661,334) .

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Frequently Asked Questions on HCF of 334, 661 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 334, 661?

Answer: HCF of 334, 661 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 334, 661 using Euclid's Algorithm?

Answer: For arbitrary numbers 334, 661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.