Highest Common Factor of 766, 976, 789 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 766, 976, 789 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 766, 976, 789 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 766, 976, 789 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 766, 976, 789 is 1.

HCF(766, 976, 789) = 1

HCF of 766, 976, 789 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 766, 976, 789 is 1.

Highest Common Factor of 766,976,789 using Euclid's algorithm

Highest Common Factor of 766,976,789 is 1

Step 1: Since 976 > 766, we apply the division lemma to 976 and 766, to get

976 = 766 x 1 + 210

Step 2: Since the reminder 766 ≠ 0, we apply division lemma to 210 and 766, to get

766 = 210 x 3 + 136

Step 3: We consider the new divisor 210 and the new remainder 136, and apply the division lemma to get

210 = 136 x 1 + 74

We consider the new divisor 136 and the new remainder 74,and apply the division lemma to get

136 = 74 x 1 + 62

We consider the new divisor 74 and the new remainder 62,and apply the division lemma to get

74 = 62 x 1 + 12

We consider the new divisor 62 and the new remainder 12,and apply the division lemma to get

62 = 12 x 5 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 766 and 976 is 2

Notice that 2 = HCF(12,2) = HCF(62,12) = HCF(74,62) = HCF(136,74) = HCF(210,136) = HCF(766,210) = HCF(976,766) .

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

Step 1: Since 789 > 2, we apply the division lemma to 789 and 2, to get

789 = 2 x 394 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 789 is 1

Notice that 1 = HCF(2,1) = HCF(789,2) .

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Frequently Asked Questions on HCF of 766, 976, 789 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 766, 976, 789?

Answer: HCF of 766, 976, 789 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 766, 976, 789 using Euclid's Algorithm?

Answer: For arbitrary numbers 766, 976, 789 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.