Highest Common Factor of 6034, 9736 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 6034, 9736 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6034, 9736 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 6034, 9736 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 6034, 9736 is 2.

HCF(6034, 9736) = 2

HCF of 6034, 9736 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 6034, 9736 is 2.

Highest Common Factor of 6034,9736 using Euclid's algorithm

Highest Common Factor of 6034,9736 is 2

Step 1: Since 9736 > 6034, we apply the division lemma to 9736 and 6034, to get

9736 = 6034 x 1 + 3702

Step 2: Since the reminder 6034 ≠ 0, we apply division lemma to 3702 and 6034, to get

6034 = 3702 x 1 + 2332

Step 3: We consider the new divisor 3702 and the new remainder 2332, and apply the division lemma to get

3702 = 2332 x 1 + 1370

We consider the new divisor 2332 and the new remainder 1370,and apply the division lemma to get

2332 = 1370 x 1 + 962

We consider the new divisor 1370 and the new remainder 962,and apply the division lemma to get

1370 = 962 x 1 + 408

We consider the new divisor 962 and the new remainder 408,and apply the division lemma to get

962 = 408 x 2 + 146

We consider the new divisor 408 and the new remainder 146,and apply the division lemma to get

408 = 146 x 2 + 116

We consider the new divisor 146 and the new remainder 116,and apply the division lemma to get

146 = 116 x 1 + 30

We consider the new divisor 116 and the new remainder 30,and apply the division lemma to get

116 = 30 x 3 + 26

We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get

30 = 26 x 1 + 4

We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get

26 = 4 x 6 + 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 6034 and 9736 is 2

Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(116,30) = HCF(146,116) = HCF(408,146) = HCF(962,408) = HCF(1370,962) = HCF(2332,1370) = HCF(3702,2332) = HCF(6034,3702) = HCF(9736,6034) .

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Frequently Asked Questions on HCF of 6034, 9736 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 6034, 9736?

Answer: HCF of 6034, 9736 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6034, 9736 using Euclid's Algorithm?

Answer: For arbitrary numbers 6034, 9736 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.