Highest Common Factor of 8522, 9498 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 8522, 9498 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 8522, 9498 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 8522, 9498 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 8522, 9498 is 2.

HCF(8522, 9498) = 2

HCF of 8522, 9498 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 8522, 9498 is 2.

Highest Common Factor of 8522,9498 using Euclid's algorithm

Highest Common Factor of 8522,9498 is 2

Step 1: Since 9498 > 8522, we apply the division lemma to 9498 and 8522, to get

9498 = 8522 x 1 + 976

Step 2: Since the reminder 8522 ≠ 0, we apply division lemma to 976 and 8522, to get

8522 = 976 x 8 + 714

Step 3: We consider the new divisor 976 and the new remainder 714, and apply the division lemma to get

976 = 714 x 1 + 262

We consider the new divisor 714 and the new remainder 262,and apply the division lemma to get

714 = 262 x 2 + 190

We consider the new divisor 262 and the new remainder 190,and apply the division lemma to get

262 = 190 x 1 + 72

We consider the new divisor 190 and the new remainder 72,and apply the division lemma to get

190 = 72 x 2 + 46

We consider the new divisor 72 and the new remainder 46,and apply the division lemma to get

72 = 46 x 1 + 26

We consider the new divisor 46 and the new remainder 26,and apply the division lemma to get

46 = 26 x 1 + 20

We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get

26 = 20 x 1 + 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 8522 and 9498 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(46,26) = HCF(72,46) = HCF(190,72) = HCF(262,190) = HCF(714,262) = HCF(976,714) = HCF(8522,976) = HCF(9498,8522) .

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Frequently Asked Questions on HCF of 8522, 9498 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 8522, 9498?

Answer: HCF of 8522, 9498 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8522, 9498 using Euclid's Algorithm?

Answer: For arbitrary numbers 8522, 9498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.