Highest Common Factor of 362, 596, 363 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 362, 596, 363 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 362, 596, 363 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 362, 596, 363 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 362, 596, 363 is 1.

HCF(362, 596, 363) = 1

HCF of 362, 596, 363 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 362, 596, 363 is 1.

Highest Common Factor of 362,596,363 using Euclid's algorithm

Highest Common Factor of 362,596,363 is 1

Step 1: Since 596 > 362, we apply the division lemma to 596 and 362, to get

596 = 362 x 1 + 234

Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 234 and 362, to get

362 = 234 x 1 + 128

Step 3: We consider the new divisor 234 and the new remainder 128, and apply the division lemma to get

234 = 128 x 1 + 106

We consider the new divisor 128 and the new remainder 106,and apply the division lemma to get

128 = 106 x 1 + 22

We consider the new divisor 106 and the new remainder 22,and apply the division lemma to get

106 = 22 x 4 + 18

We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get

22 = 18 x 1 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 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 362 and 596 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(106,22) = HCF(128,106) = HCF(234,128) = HCF(362,234) = HCF(596,362) .

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

Step 1: Since 363 > 2, we apply the division lemma to 363 and 2, to get

363 = 2 x 181 + 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 363 is 1

Notice that 1 = HCF(2,1) = HCF(363,2) .

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Frequently Asked Questions on HCF of 362, 596, 363 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 362, 596, 363?

Answer: HCF of 362, 596, 363 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 362, 596, 363 using Euclid's Algorithm?

Answer: For arbitrary numbers 362, 596, 363 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.