Highest Common Factor of 762, 482, 67 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, 482, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 762, 482, 67 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, 482, 67 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, 482, 67 is 1.

HCF(762, 482, 67) = 1

HCF of 762, 482, 67 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, 482, 67 is 1.

Highest Common Factor of 762,482,67 using Euclid's algorithm

Highest Common Factor of 762,482,67 is 1

Step 1: Since 762 > 482, we apply the division lemma to 762 and 482, to get

762 = 482 x 1 + 280

Step 2: Since the reminder 482 ≠ 0, we apply division lemma to 280 and 482, to get

482 = 280 x 1 + 202

Step 3: We consider the new divisor 280 and the new remainder 202, and apply the division lemma to get

280 = 202 x 1 + 78

We consider the new divisor 202 and the new remainder 78,and apply the division lemma to get

202 = 78 x 2 + 46

We consider the new divisor 78 and the new remainder 46,and apply the division lemma to get

78 = 46 x 1 + 32

We consider the new divisor 46 and the new remainder 32,and apply the division lemma to get

46 = 32 x 1 + 14

We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get

32 = 14 x 2 + 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 482 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(46,32) = HCF(78,46) = HCF(202,78) = HCF(280,202) = HCF(482,280) = HCF(762,482) .

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

Step 1: Since 67 > 2, we apply the division lemma to 67 and 2, to get

67 = 2 x 33 + 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 67 is 1

Notice that 1 = HCF(2,1) = HCF(67,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 762, 482, 67 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, 482, 67?

Answer: HCF of 762, 482, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 762, 482, 67 using Euclid's Algorithm?

Answer: For arbitrary numbers 762, 482, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.