Highest Common Factor of 9630, 2074 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 9630, 2074 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 9630, 2074 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 9630, 2074 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 9630, 2074 is 2.

HCF(9630, 2074) = 2

HCF of 9630, 2074 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 9630, 2074 is 2.

Highest Common Factor of 9630,2074 using Euclid's algorithm

Highest Common Factor of 9630,2074 is 2

Step 1: Since 9630 > 2074, we apply the division lemma to 9630 and 2074, to get

9630 = 2074 x 4 + 1334

Step 2: Since the reminder 2074 ≠ 0, we apply division lemma to 1334 and 2074, to get

2074 = 1334 x 1 + 740

Step 3: We consider the new divisor 1334 and the new remainder 740, and apply the division lemma to get

1334 = 740 x 1 + 594

We consider the new divisor 740 and the new remainder 594,and apply the division lemma to get

740 = 594 x 1 + 146

We consider the new divisor 594 and the new remainder 146,and apply the division lemma to get

594 = 146 x 4 + 10

We consider the new divisor 146 and the new remainder 10,and apply the division lemma to get

146 = 10 x 14 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 9630 and 2074 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(146,10) = HCF(594,146) = HCF(740,594) = HCF(1334,740) = HCF(2074,1334) = HCF(9630,2074) .

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Frequently Asked Questions on HCF of 9630, 2074 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 9630, 2074?

Answer: HCF of 9630, 2074 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9630, 2074 using Euclid's Algorithm?

Answer: For arbitrary numbers 9630, 2074 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.