Highest Common Factor of 749, 3462 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 749, 3462 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 749, 3462 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 749, 3462 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 749, 3462 is 1.

HCF(749, 3462) = 1

HCF of 749, 3462 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 749, 3462 is 1.

Highest Common Factor of 749,3462 using Euclid's algorithm

Highest Common Factor of 749,3462 is 1

Step 1: Since 3462 > 749, we apply the division lemma to 3462 and 749, to get

3462 = 749 x 4 + 466

Step 2: Since the reminder 749 ≠ 0, we apply division lemma to 466 and 749, to get

749 = 466 x 1 + 283

Step 3: We consider the new divisor 466 and the new remainder 283, and apply the division lemma to get

466 = 283 x 1 + 183

We consider the new divisor 283 and the new remainder 183,and apply the division lemma to get

283 = 183 x 1 + 100

We consider the new divisor 183 and the new remainder 100,and apply the division lemma to get

183 = 100 x 1 + 83

We consider the new divisor 100 and the new remainder 83,and apply the division lemma to get

100 = 83 x 1 + 17

We consider the new divisor 83 and the new remainder 17,and apply the division lemma to get

83 = 17 x 4 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 749 and 3462 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(83,17) = HCF(100,83) = HCF(183,100) = HCF(283,183) = HCF(466,283) = HCF(749,466) = HCF(3462,749) .

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Frequently Asked Questions on HCF of 749, 3462 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 749, 3462?

Answer: HCF of 749, 3462 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 749, 3462 using Euclid's Algorithm?

Answer: For arbitrary numbers 749, 3462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.