Highest Common Factor of 966, 378, 989 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, 378, 989 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 966, 378, 989 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, 378, 989 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, 378, 989 is 1.

HCF(966, 378, 989) = 1

HCF of 966, 378, 989 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, 378, 989 is 1.

Highest Common Factor of 966,378,989 using Euclid's algorithm

Highest Common Factor of 966,378,989 is 1

Step 1: Since 966 > 378, we apply the division lemma to 966 and 378, to get

966 = 378 x 2 + 210

Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 210 and 378, to get

378 = 210 x 1 + 168

Step 3: We consider the new divisor 210 and the new remainder 168, and apply the division lemma to get

210 = 168 x 1 + 42

We consider the new divisor 168 and the new remainder 42, and apply the division lemma to get

168 = 42 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 966 and 378 is 42

Notice that 42 = HCF(168,42) = HCF(210,168) = HCF(378,210) = HCF(966,378) .

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

Step 1: Since 989 > 42, we apply the division lemma to 989 and 42, to get

989 = 42 x 23 + 23

Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 23 and 42, to get

42 = 23 x 1 + 19

Step 3: We consider the new divisor 23 and the new remainder 19, and apply the division lemma to get

23 = 19 x 1 + 4

We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get

19 = 4 x 4 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 42 and 989 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(23,19) = HCF(42,23) = HCF(989,42) .

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Frequently Asked Questions on HCF of 966, 378, 989 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, 378, 989?

Answer: HCF of 966, 378, 989 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 966, 378, 989 using Euclid's Algorithm?

Answer: For arbitrary numbers 966, 378, 989 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.