Highest Common Factor of 722, 457, 500 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 722, 457, 500 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 722, 457, 500 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 722, 457, 500 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 722, 457, 500 is 1.

HCF(722, 457, 500) = 1

HCF of 722, 457, 500 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 722, 457, 500 is 1.

Highest Common Factor of 722,457,500 using Euclid's algorithm

Highest Common Factor of 722,457,500 is 1

Step 1: Since 722 > 457, we apply the division lemma to 722 and 457, to get

722 = 457 x 1 + 265

Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 265 and 457, to get

457 = 265 x 1 + 192

Step 3: We consider the new divisor 265 and the new remainder 192, and apply the division lemma to get

265 = 192 x 1 + 73

We consider the new divisor 192 and the new remainder 73,and apply the division lemma to get

192 = 73 x 2 + 46

We consider the new divisor 73 and the new remainder 46,and apply the division lemma to get

73 = 46 x 1 + 27

We consider the new divisor 46 and the new remainder 27,and apply the division lemma to get

46 = 27 x 1 + 19

We consider the new divisor 27 and the new remainder 19,and apply the division lemma to get

27 = 19 x 1 + 8

We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get

19 = 8 x 2 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 722 and 457 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(46,27) = HCF(73,46) = HCF(192,73) = HCF(265,192) = HCF(457,265) = HCF(722,457) .

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

Step 1: Since 500 > 1, we apply the division lemma to 500 and 1, to get

500 = 1 x 500 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 500 is 1

Notice that 1 = HCF(500,1) .

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Frequently Asked Questions on HCF of 722, 457, 500 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 722, 457, 500?

Answer: HCF of 722, 457, 500 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 722, 457, 500 using Euclid's Algorithm?

Answer: For arbitrary numbers 722, 457, 500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.