Highest Common Factor of 8574, 9919 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 8574, 9919 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8574, 9919 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 8574, 9919 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 8574, 9919 is 1.

HCF(8574, 9919) = 1

HCF of 8574, 9919 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 8574, 9919 is 1.

Highest Common Factor of 8574,9919 using Euclid's algorithm

Highest Common Factor of 8574,9919 is 1

Step 1: Since 9919 > 8574, we apply the division lemma to 9919 and 8574, to get

9919 = 8574 x 1 + 1345

Step 2: Since the reminder 8574 ≠ 0, we apply division lemma to 1345 and 8574, to get

8574 = 1345 x 6 + 504

Step 3: We consider the new divisor 1345 and the new remainder 504, and apply the division lemma to get

1345 = 504 x 2 + 337

We consider the new divisor 504 and the new remainder 337,and apply the division lemma to get

504 = 337 x 1 + 167

We consider the new divisor 337 and the new remainder 167,and apply the division lemma to get

337 = 167 x 2 + 3

We consider the new divisor 167 and the new remainder 3,and apply the division lemma to get

167 = 3 x 55 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 8574 and 9919 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(167,3) = HCF(337,167) = HCF(504,337) = HCF(1345,504) = HCF(8574,1345) = HCF(9919,8574) .

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Frequently Asked Questions on HCF of 8574, 9919 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 8574, 9919?

Answer: HCF of 8574, 9919 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8574, 9919 using Euclid's Algorithm?

Answer: For arbitrary numbers 8574, 9919 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.