Highest Common Factor of 7356, 9322, 10610 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 7356, 9322, 10610 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 7356, 9322, 10610 is 2 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 7356, 9322, 10610 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 7356, 9322, 10610 is 2.

HCF(7356, 9322, 10610) = 2

HCF of 7356, 9322, 10610 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 7356, 9322, 10610 is 2.

Highest Common Factor of 7356,9322,10610 using Euclid's algorithm

Highest Common Factor of 7356,9322,10610 is 2

Step 1: Since 9322 > 7356, we apply the division lemma to 9322 and 7356, to get

9322 = 7356 x 1 + 1966

Step 2: Since the reminder 7356 ≠ 0, we apply division lemma to 1966 and 7356, to get

7356 = 1966 x 3 + 1458

Step 3: We consider the new divisor 1966 and the new remainder 1458, and apply the division lemma to get

1966 = 1458 x 1 + 508

We consider the new divisor 1458 and the new remainder 508,and apply the division lemma to get

1458 = 508 x 2 + 442

We consider the new divisor 508 and the new remainder 442,and apply the division lemma to get

508 = 442 x 1 + 66

We consider the new divisor 442 and the new remainder 66,and apply the division lemma to get

442 = 66 x 6 + 46

We consider the new divisor 66 and the new remainder 46,and apply the division lemma to get

66 = 46 x 1 + 20

We consider the new divisor 46 and the new remainder 20,and apply the division lemma to get

46 = 20 x 2 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7356 and 9322 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(46,20) = HCF(66,46) = HCF(442,66) = HCF(508,442) = HCF(1458,508) = HCF(1966,1458) = HCF(7356,1966) = HCF(9322,7356) .

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

Step 1: Since 10610 > 2, we apply the division lemma to 10610 and 2, to get

10610 = 2 x 5305 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 10610 is 2

Notice that 2 = HCF(10610,2) .

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Frequently Asked Questions on HCF of 7356, 9322, 10610 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 7356, 9322, 10610?

Answer: HCF of 7356, 9322, 10610 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7356, 9322, 10610 using Euclid's Algorithm?

Answer: For arbitrary numbers 7356, 9322, 10610 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.