Highest Common Factor of 9636, 6922, 77049 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 9636, 6922, 77049 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9636, 6922, 77049 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 9636, 6922, 77049 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 9636, 6922, 77049 is 1.

HCF(9636, 6922, 77049) = 1

HCF of 9636, 6922, 77049 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 9636, 6922, 77049 is 1.

Highest Common Factor of 9636,6922,77049 using Euclid's algorithm

Highest Common Factor of 9636,6922,77049 is 1

Step 1: Since 9636 > 6922, we apply the division lemma to 9636 and 6922, to get

9636 = 6922 x 1 + 2714

Step 2: Since the reminder 6922 ≠ 0, we apply division lemma to 2714 and 6922, to get

6922 = 2714 x 2 + 1494

Step 3: We consider the new divisor 2714 and the new remainder 1494, and apply the division lemma to get

2714 = 1494 x 1 + 1220

We consider the new divisor 1494 and the new remainder 1220,and apply the division lemma to get

1494 = 1220 x 1 + 274

We consider the new divisor 1220 and the new remainder 274,and apply the division lemma to get

1220 = 274 x 4 + 124

We consider the new divisor 274 and the new remainder 124,and apply the division lemma to get

274 = 124 x 2 + 26

We consider the new divisor 124 and the new remainder 26,and apply the division lemma to get

124 = 26 x 4 + 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 9636 and 6922 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(124,26) = HCF(274,124) = HCF(1220,274) = HCF(1494,1220) = HCF(2714,1494) = HCF(6922,2714) = HCF(9636,6922) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 77049 > 2, we apply the division lemma to 77049 and 2, to get

77049 = 2 x 38524 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 77049 is 1

Notice that 1 = HCF(2,1) = HCF(77049,2) .

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Frequently Asked Questions on HCF of 9636, 6922, 77049 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 9636, 6922, 77049?

Answer: HCF of 9636, 6922, 77049 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9636, 6922, 77049 using Euclid's Algorithm?

Answer: For arbitrary numbers 9636, 6922, 77049 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.