Highest Common Factor of 966, 523, 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 966, 523, 661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 966, 523, 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 966, 523, 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 966, 523, 661 is 1.

HCF(966, 523, 661) = 1

HCF of 966, 523, 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 966, 523, 661 is 1.

Highest Common Factor of 966,523,661 using Euclid's algorithm

Highest Common Factor of 966,523,661 is 1

Step 1: Since 966 > 523, we apply the division lemma to 966 and 523, to get

966 = 523 x 1 + 443

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 443 and 523, to get

523 = 443 x 1 + 80

Step 3: We consider the new divisor 443 and the new remainder 80, and apply the division lemma to get

443 = 80 x 5 + 43

We consider the new divisor 80 and the new remainder 43,and apply the division lemma to get

80 = 43 x 1 + 37

We consider the new divisor 43 and the new remainder 37,and apply the division lemma to get

43 = 37 x 1 + 6

We consider the new divisor 37 and the new remainder 6,and apply the division lemma to get

37 = 6 x 6 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 966 and 523 is 1

Notice that 1 = HCF(6,1) = HCF(37,6) = HCF(43,37) = HCF(80,43) = HCF(443,80) = HCF(523,443) = HCF(966,523) .

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

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

661 = 1 x 661 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 661 is 1

Notice that 1 = HCF(661,1) .

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Frequently Asked Questions on HCF of 966, 523, 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 966, 523, 661?

Answer: HCF of 966, 523, 661 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 966, 523, 661 using Euclid's Algorithm?

Answer: For arbitrary numbers 966, 523, 661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.