Highest Common Factor of 708, 441, 497 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 708, 441, 497 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 708, 441, 497 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 708, 441, 497 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 708, 441, 497 is 1.

HCF(708, 441, 497) = 1

HCF of 708, 441, 497 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 708, 441, 497 is 1.

Highest Common Factor of 708,441,497 using Euclid's algorithm

Highest Common Factor of 708,441,497 is 1

Step 1: Since 708 > 441, we apply the division lemma to 708 and 441, to get

708 = 441 x 1 + 267

Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 267 and 441, to get

441 = 267 x 1 + 174

Step 3: We consider the new divisor 267 and the new remainder 174, and apply the division lemma to get

267 = 174 x 1 + 93

We consider the new divisor 174 and the new remainder 93,and apply the division lemma to get

174 = 93 x 1 + 81

We consider the new divisor 93 and the new remainder 81,and apply the division lemma to get

93 = 81 x 1 + 12

We consider the new divisor 81 and the new remainder 12,and apply the division lemma to get

81 = 12 x 6 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 708 and 441 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(81,12) = HCF(93,81) = HCF(174,93) = HCF(267,174) = HCF(441,267) = HCF(708,441) .

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

Step 1: Since 497 > 3, we apply the division lemma to 497 and 3, to get

497 = 3 x 165 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 497 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(497,3) .

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Frequently Asked Questions on HCF of 708, 441, 497 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 708, 441, 497?

Answer: HCF of 708, 441, 497 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 708, 441, 497 using Euclid's Algorithm?

Answer: For arbitrary numbers 708, 441, 497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.