Highest Common Factor of 732, 458, 353 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 732, 458, 353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 732, 458, 353 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 732, 458, 353 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 732, 458, 353 is 1.

HCF(732, 458, 353) = 1

HCF of 732, 458, 353 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 732, 458, 353 is 1.

Highest Common Factor of 732,458,353 using Euclid's algorithm

Highest Common Factor of 732,458,353 is 1

Step 1: Since 732 > 458, we apply the division lemma to 732 and 458, to get

732 = 458 x 1 + 274

Step 2: Since the reminder 458 ≠ 0, we apply division lemma to 274 and 458, to get

458 = 274 x 1 + 184

Step 3: We consider the new divisor 274 and the new remainder 184, and apply the division lemma to get

274 = 184 x 1 + 90

We consider the new divisor 184 and the new remainder 90,and apply the division lemma to get

184 = 90 x 2 + 4

We consider the new divisor 90 and the new remainder 4,and apply the division lemma to get

90 = 4 x 22 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 732 and 458 is 2

Notice that 2 = HCF(4,2) = HCF(90,4) = HCF(184,90) = HCF(274,184) = HCF(458,274) = HCF(732,458) .

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

Step 1: Since 353 > 2, we apply the division lemma to 353 and 2, to get

353 = 2 x 176 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 353 is 1

Notice that 1 = HCF(2,1) = HCF(353,2) .

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Frequently Asked Questions on HCF of 732, 458, 353 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 732, 458, 353?

Answer: HCF of 732, 458, 353 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 732, 458, 353 using Euclid's Algorithm?

Answer: For arbitrary numbers 732, 458, 353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.