Highest Common Factor of 741, 458 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 741, 458 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 741, 458 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 741, 458 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 741, 458 is 1.

HCF(741, 458) = 1

HCF of 741, 458 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 741, 458 is 1.

Highest Common Factor of 741,458 using Euclid's algorithm

Highest Common Factor of 741,458 is 1

Step 1: Since 741 > 458, we apply the division lemma to 741 and 458, to get

741 = 458 x 1 + 283

Step 2: Since the reminder 458 ≠ 0, we apply division lemma to 283 and 458, to get

458 = 283 x 1 + 175

Step 3: We consider the new divisor 283 and the new remainder 175, and apply the division lemma to get

283 = 175 x 1 + 108

We consider the new divisor 175 and the new remainder 108,and apply the division lemma to get

175 = 108 x 1 + 67

We consider the new divisor 108 and the new remainder 67,and apply the division lemma to get

108 = 67 x 1 + 41

We consider the new divisor 67 and the new remainder 41,and apply the division lemma to get

67 = 41 x 1 + 26

We consider the new divisor 41 and the new remainder 26,and apply the division lemma to get

41 = 26 x 1 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 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 741 and 458 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(41,26) = HCF(67,41) = HCF(108,67) = HCF(175,108) = HCF(283,175) = HCF(458,283) = HCF(741,458) .

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Frequently Asked Questions on HCF of 741, 458 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 741, 458?

Answer: HCF of 741, 458 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 741, 458 using Euclid's Algorithm?

Answer: For arbitrary numbers 741, 458 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.