Highest Common Factor of 737, 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 737, 457 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 737, 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 737, 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 737, 457 is 1.

HCF(737, 457) = 1

HCF of 737, 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 737, 457 is 1.

Highest Common Factor of 737,457 using Euclid's algorithm

Highest Common Factor of 737,457 is 1

Step 1: Since 737 > 457, we apply the division lemma to 737 and 457, to get

737 = 457 x 1 + 280

Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 280 and 457, to get

457 = 280 x 1 + 177

Step 3: We consider the new divisor 280 and the new remainder 177, and apply the division lemma to get

280 = 177 x 1 + 103

We consider the new divisor 177 and the new remainder 103,and apply the division lemma to get

177 = 103 x 1 + 74

We consider the new divisor 103 and the new remainder 74,and apply the division lemma to get

103 = 74 x 1 + 29

We consider the new divisor 74 and the new remainder 29,and apply the division lemma to get

74 = 29 x 2 + 16

We consider the new divisor 29 and the new remainder 16,and apply the division lemma to get

29 = 16 x 1 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 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 737 and 457 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(29,16) = HCF(74,29) = HCF(103,74) = HCF(177,103) = HCF(280,177) = HCF(457,280) = HCF(737,457) .

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Frequently Asked Questions on HCF of 737, 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 737, 457?

Answer: HCF of 737, 457 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 737, 457 using Euclid's Algorithm?

Answer: For arbitrary numbers 737, 457 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.