Highest Common Factor of 9963, 4216, 77874 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 9963, 4216, 77874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9963, 4216, 77874 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 9963, 4216, 77874 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 9963, 4216, 77874 is 1.

HCF(9963, 4216, 77874) = 1

HCF of 9963, 4216, 77874 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 9963, 4216, 77874 is 1.

Highest Common Factor of 9963,4216,77874 using Euclid's algorithm

Highest Common Factor of 9963,4216,77874 is 1

Step 1: Since 9963 > 4216, we apply the division lemma to 9963 and 4216, to get

9963 = 4216 x 2 + 1531

Step 2: Since the reminder 4216 ≠ 0, we apply division lemma to 1531 and 4216, to get

4216 = 1531 x 2 + 1154

Step 3: We consider the new divisor 1531 and the new remainder 1154, and apply the division lemma to get

1531 = 1154 x 1 + 377

We consider the new divisor 1154 and the new remainder 377,and apply the division lemma to get

1154 = 377 x 3 + 23

We consider the new divisor 377 and the new remainder 23,and apply the division lemma to get

377 = 23 x 16 + 9

We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get

23 = 9 x 2 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9963 and 4216 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(377,23) = HCF(1154,377) = HCF(1531,1154) = HCF(4216,1531) = HCF(9963,4216) .

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

Step 1: Since 77874 > 1, we apply the division lemma to 77874 and 1, to get

77874 = 1 x 77874 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77874 is 1

Notice that 1 = HCF(77874,1) .

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Frequently Asked Questions on HCF of 9963, 4216, 77874 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 9963, 4216, 77874?

Answer: HCF of 9963, 4216, 77874 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9963, 4216, 77874 using Euclid's Algorithm?

Answer: For arbitrary numbers 9963, 4216, 77874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.