Highest Common Factor of 8286, 9224, 30355 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 8286, 9224, 30355 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8286, 9224, 30355 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 8286, 9224, 30355 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 8286, 9224, 30355 is 1.

HCF(8286, 9224, 30355) = 1

HCF of 8286, 9224, 30355 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 8286, 9224, 30355 is 1.

Highest Common Factor of 8286,9224,30355 using Euclid's algorithm

Highest Common Factor of 8286,9224,30355 is 1

Step 1: Since 9224 > 8286, we apply the division lemma to 9224 and 8286, to get

9224 = 8286 x 1 + 938

Step 2: Since the reminder 8286 ≠ 0, we apply division lemma to 938 and 8286, to get

8286 = 938 x 8 + 782

Step 3: We consider the new divisor 938 and the new remainder 782, and apply the division lemma to get

938 = 782 x 1 + 156

We consider the new divisor 782 and the new remainder 156,and apply the division lemma to get

782 = 156 x 5 + 2

We consider the new divisor 156 and the new remainder 2,and apply the division lemma to get

156 = 2 x 78 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8286 and 9224 is 2

Notice that 2 = HCF(156,2) = HCF(782,156) = HCF(938,782) = HCF(8286,938) = HCF(9224,8286) .

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

Step 1: Since 30355 > 2, we apply the division lemma to 30355 and 2, to get

30355 = 2 x 15177 + 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 30355 is 1

Notice that 1 = HCF(2,1) = HCF(30355,2) .

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Frequently Asked Questions on HCF of 8286, 9224, 30355 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 8286, 9224, 30355?

Answer: HCF of 8286, 9224, 30355 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8286, 9224, 30355 using Euclid's Algorithm?

Answer: For arbitrary numbers 8286, 9224, 30355 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.