Highest Common Factor of 459, 728, 362 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 459, 728, 362 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 459, 728, 362 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 459, 728, 362 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 459, 728, 362 is 1.

HCF(459, 728, 362) = 1

HCF of 459, 728, 362 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 459, 728, 362 is 1.

Highest Common Factor of 459,728,362 using Euclid's algorithm

Highest Common Factor of 459,728,362 is 1

Step 1: Since 728 > 459, we apply the division lemma to 728 and 459, to get

728 = 459 x 1 + 269

Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 269 and 459, to get

459 = 269 x 1 + 190

Step 3: We consider the new divisor 269 and the new remainder 190, and apply the division lemma to get

269 = 190 x 1 + 79

We consider the new divisor 190 and the new remainder 79,and apply the division lemma to get

190 = 79 x 2 + 32

We consider the new divisor 79 and the new remainder 32,and apply the division lemma to get

79 = 32 x 2 + 15

We consider the new divisor 32 and the new remainder 15,and apply the division lemma to get

32 = 15 x 2 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 459 and 728 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(32,15) = HCF(79,32) = HCF(190,79) = HCF(269,190) = HCF(459,269) = HCF(728,459) .

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

Step 1: Since 362 > 1, we apply the division lemma to 362 and 1, to get

362 = 1 x 362 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 362 is 1

Notice that 1 = HCF(362,1) .

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Frequently Asked Questions on HCF of 459, 728, 362 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 459, 728, 362?

Answer: HCF of 459, 728, 362 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 459, 728, 362 using Euclid's Algorithm?

Answer: For arbitrary numbers 459, 728, 362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.