Highest Common Factor of 362, 7786, 8297 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, 7786, 8297 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 362, 7786, 8297 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, 7786, 8297 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, 7786, 8297 is 1.

HCF(362, 7786, 8297) = 1

HCF of 362, 7786, 8297 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, 7786, 8297 is 1.

Highest Common Factor of 362,7786,8297 using Euclid's algorithm

Highest Common Factor of 362,7786,8297 is 1

Step 1: Since 7786 > 362, we apply the division lemma to 7786 and 362, to get

7786 = 362 x 21 + 184

Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 184 and 362, to get

362 = 184 x 1 + 178

Step 3: We consider the new divisor 184 and the new remainder 178, and apply the division lemma to get

184 = 178 x 1 + 6

We consider the new divisor 178 and the new remainder 6,and apply the division lemma to get

178 = 6 x 29 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 7786 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(178,6) = HCF(184,178) = HCF(362,184) = HCF(7786,362) .

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

Step 1: Since 8297 > 2, we apply the division lemma to 8297 and 2, to get

8297 = 2 x 4148 + 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 8297 is 1

Notice that 1 = HCF(2,1) = HCF(8297,2) .

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Frequently Asked Questions on HCF of 362, 7786, 8297 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, 7786, 8297?

Answer: HCF of 362, 7786, 8297 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 362, 7786, 8297 using Euclid's Algorithm?

Answer: For arbitrary numbers 362, 7786, 8297 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.