Highest Common Factor of 770, 22734 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 770, 22734 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 770, 22734 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 770, 22734 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 770, 22734 is 2.

HCF(770, 22734) = 2

HCF of 770, 22734 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 770, 22734 is 2.

Highest Common Factor of 770,22734 using Euclid's algorithm

Highest Common Factor of 770,22734 is 2

Step 1: Since 22734 > 770, we apply the division lemma to 22734 and 770, to get

22734 = 770 x 29 + 404

Step 2: Since the reminder 770 ≠ 0, we apply division lemma to 404 and 770, to get

770 = 404 x 1 + 366

Step 3: We consider the new divisor 404 and the new remainder 366, and apply the division lemma to get

404 = 366 x 1 + 38

We consider the new divisor 366 and the new remainder 38,and apply the division lemma to get

366 = 38 x 9 + 24

We consider the new divisor 38 and the new remainder 24,and apply the division lemma to get

38 = 24 x 1 + 14

We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get

24 = 14 x 1 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 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 770 and 22734 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(38,24) = HCF(366,38) = HCF(404,366) = HCF(770,404) = HCF(22734,770) .

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Frequently Asked Questions on HCF of 770, 22734 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 770, 22734?

Answer: HCF of 770, 22734 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 770, 22734 using Euclid's Algorithm?

Answer: For arbitrary numbers 770, 22734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.