Highest Common Factor of 457, 285, 722 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 457, 285, 722 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 457, 285, 722 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 457, 285, 722 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 457, 285, 722 is 1.

HCF(457, 285, 722) = 1

HCF of 457, 285, 722 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 457, 285, 722 is 1.

Highest Common Factor of 457,285,722 using Euclid's algorithm

Highest Common Factor of 457,285,722 is 1

Step 1: Since 457 > 285, we apply the division lemma to 457 and 285, to get

457 = 285 x 1 + 172

Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 172 and 285, to get

285 = 172 x 1 + 113

Step 3: We consider the new divisor 172 and the new remainder 113, and apply the division lemma to get

172 = 113 x 1 + 59

We consider the new divisor 113 and the new remainder 59,and apply the division lemma to get

113 = 59 x 1 + 54

We consider the new divisor 59 and the new remainder 54,and apply the division lemma to get

59 = 54 x 1 + 5

We consider the new divisor 54 and the new remainder 5,and apply the division lemma to get

54 = 5 x 10 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 285 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(54,5) = HCF(59,54) = HCF(113,59) = HCF(172,113) = HCF(285,172) = HCF(457,285) .

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

Step 1: Since 722 > 1, we apply the division lemma to 722 and 1, to get

722 = 1 x 722 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 722 is 1

Notice that 1 = HCF(722,1) .

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Frequently Asked Questions on HCF of 457, 285, 722 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 457, 285, 722?

Answer: HCF of 457, 285, 722 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 457, 285, 722 using Euclid's Algorithm?

Answer: For arbitrary numbers 457, 285, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.