Highest Common Factor of 998, 606, 963 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 998, 606, 963 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 998, 606, 963 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 998, 606, 963 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 998, 606, 963 is 1.

HCF(998, 606, 963) = 1

HCF of 998, 606, 963 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 998, 606, 963 is 1.

Highest Common Factor of 998,606,963 using Euclid's algorithm

Highest Common Factor of 998,606,963 is 1

Step 1: Since 998 > 606, we apply the division lemma to 998 and 606, to get

998 = 606 x 1 + 392

Step 2: Since the reminder 606 ≠ 0, we apply division lemma to 392 and 606, to get

606 = 392 x 1 + 214

Step 3: We consider the new divisor 392 and the new remainder 214, and apply the division lemma to get

392 = 214 x 1 + 178

We consider the new divisor 214 and the new remainder 178,and apply the division lemma to get

214 = 178 x 1 + 36

We consider the new divisor 178 and the new remainder 36,and apply the division lemma to get

178 = 36 x 4 + 34

We consider the new divisor 36 and the new remainder 34,and apply the division lemma to get

36 = 34 x 1 + 2

We consider the new divisor 34 and the new remainder 2,and apply the division lemma to get

34 = 2 x 17 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 998 and 606 is 2

Notice that 2 = HCF(34,2) = HCF(36,34) = HCF(178,36) = HCF(214,178) = HCF(392,214) = HCF(606,392) = HCF(998,606) .

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

Step 1: Since 963 > 2, we apply the division lemma to 963 and 2, to get

963 = 2 x 481 + 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 963 is 1

Notice that 1 = HCF(2,1) = HCF(963,2) .

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Frequently Asked Questions on HCF of 998, 606, 963 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 998, 606, 963?

Answer: HCF of 998, 606, 963 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 998, 606, 963 using Euclid's Algorithm?

Answer: For arbitrary numbers 998, 606, 963 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.