Highest Common Factor of 996, 577, 215 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 996, 577, 215 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 996, 577, 215 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 996, 577, 215 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 996, 577, 215 is 1.

HCF(996, 577, 215) = 1

HCF of 996, 577, 215 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 996, 577, 215 is 1.

Highest Common Factor of 996,577,215 using Euclid's algorithm

Highest Common Factor of 996,577,215 is 1

Step 1: Since 996 > 577, we apply the division lemma to 996 and 577, to get

996 = 577 x 1 + 419

Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 419 and 577, to get

577 = 419 x 1 + 158

Step 3: We consider the new divisor 419 and the new remainder 158, and apply the division lemma to get

419 = 158 x 2 + 103

We consider the new divisor 158 and the new remainder 103,and apply the division lemma to get

158 = 103 x 1 + 55

We consider the new divisor 103 and the new remainder 55,and apply the division lemma to get

103 = 55 x 1 + 48

We consider the new divisor 55 and the new remainder 48,and apply the division lemma to get

55 = 48 x 1 + 7

We consider the new divisor 48 and the new remainder 7,and apply the division lemma to get

48 = 7 x 6 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 996 and 577 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(48,7) = HCF(55,48) = HCF(103,55) = HCF(158,103) = HCF(419,158) = HCF(577,419) = HCF(996,577) .

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

Step 1: Since 215 > 1, we apply the division lemma to 215 and 1, to get

215 = 1 x 215 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 215 is 1

Notice that 1 = HCF(215,1) .

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Frequently Asked Questions on HCF of 996, 577, 215 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 996, 577, 215?

Answer: HCF of 996, 577, 215 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 996, 577, 215 using Euclid's Algorithm?

Answer: For arbitrary numbers 996, 577, 215 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.