Highest Common Factor of 741, 457 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, 457 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 741, 457 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, 457 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, 457 is 1.

HCF(741, 457) = 1

HCF of 741, 457 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, 457 is 1.

Highest Common Factor of 741,457 using Euclid's algorithm

Highest Common Factor of 741,457 is 1

Step 1: Since 741 > 457, we apply the division lemma to 741 and 457, to get

741 = 457 x 1 + 284

Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 284 and 457, to get

457 = 284 x 1 + 173

Step 3: We consider the new divisor 284 and the new remainder 173, and apply the division lemma to get

284 = 173 x 1 + 111

We consider the new divisor 173 and the new remainder 111,and apply the division lemma to get

173 = 111 x 1 + 62

We consider the new divisor 111 and the new remainder 62,and apply the division lemma to get

111 = 62 x 1 + 49

We consider the new divisor 62 and the new remainder 49,and apply the division lemma to get

62 = 49 x 1 + 13

We consider the new divisor 49 and the new remainder 13,and apply the division lemma to get

49 = 13 x 3 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 457 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(49,13) = HCF(62,49) = HCF(111,62) = HCF(173,111) = HCF(284,173) = HCF(457,284) = HCF(741,457) .

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Frequently Asked Questions on HCF of 741, 457 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, 457?

Answer: HCF of 741, 457 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 741, 457 using Euclid's Algorithm?

Answer: For arbitrary numbers 741, 457 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.