Highest Common Factor of 598, 963, 206 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 598, 963, 206 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 598, 963, 206 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 598, 963, 206 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 598, 963, 206 is 1.

HCF(598, 963, 206) = 1

HCF of 598, 963, 206 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 598, 963, 206 is 1.

Highest Common Factor of 598,963,206 using Euclid's algorithm

Highest Common Factor of 598,963,206 is 1

Step 1: Since 963 > 598, we apply the division lemma to 963 and 598, to get

963 = 598 x 1 + 365

Step 2: Since the reminder 598 ≠ 0, we apply division lemma to 365 and 598, to get

598 = 365 x 1 + 233

Step 3: We consider the new divisor 365 and the new remainder 233, and apply the division lemma to get

365 = 233 x 1 + 132

We consider the new divisor 233 and the new remainder 132,and apply the division lemma to get

233 = 132 x 1 + 101

We consider the new divisor 132 and the new remainder 101,and apply the division lemma to get

132 = 101 x 1 + 31

We consider the new divisor 101 and the new remainder 31,and apply the division lemma to get

101 = 31 x 3 + 8

We consider the new divisor 31 and the new remainder 8,and apply the division lemma to get

31 = 8 x 3 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 598 and 963 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31,8) = HCF(101,31) = HCF(132,101) = HCF(233,132) = HCF(365,233) = HCF(598,365) = HCF(963,598) .

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

Step 1: Since 206 > 1, we apply the division lemma to 206 and 1, to get

206 = 1 x 206 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 206 is 1

Notice that 1 = HCF(206,1) .

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Frequently Asked Questions on HCF of 598, 963, 206 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 598, 963, 206?

Answer: HCF of 598, 963, 206 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 598, 963, 206 using Euclid's Algorithm?

Answer: For arbitrary numbers 598, 963, 206 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.