Highest Common Factor of 762, 460, 967 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 762, 460, 967 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 762, 460, 967 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 762, 460, 967 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 762, 460, 967 is 1.

HCF(762, 460, 967) = 1

HCF of 762, 460, 967 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 762, 460, 967 is 1.

Highest Common Factor of 762,460,967 using Euclid's algorithm

Highest Common Factor of 762,460,967 is 1

Step 1: Since 762 > 460, we apply the division lemma to 762 and 460, to get

762 = 460 x 1 + 302

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 302 and 460, to get

460 = 302 x 1 + 158

Step 3: We consider the new divisor 302 and the new remainder 158, and apply the division lemma to get

302 = 158 x 1 + 144

We consider the new divisor 158 and the new remainder 144,and apply the division lemma to get

158 = 144 x 1 + 14

We consider the new divisor 144 and the new remainder 14,and apply the division lemma to get

144 = 14 x 10 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 762 and 460 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(144,14) = HCF(158,144) = HCF(302,158) = HCF(460,302) = HCF(762,460) .

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

Step 1: Since 967 > 2, we apply the division lemma to 967 and 2, to get

967 = 2 x 483 + 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 967 is 1

Notice that 1 = HCF(2,1) = HCF(967,2) .

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Frequently Asked Questions on HCF of 762, 460, 967 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 762, 460, 967?

Answer: HCF of 762, 460, 967 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 762, 460, 967 using Euclid's Algorithm?

Answer: For arbitrary numbers 762, 460, 967 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.