Highest Common Factor of 918, 596, 198 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 918, 596, 198 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 918, 596, 198 is 2 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 918, 596, 198 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 918, 596, 198 is 2.

HCF(918, 596, 198) = 2

HCF of 918, 596, 198 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 918, 596, 198 is 2.

Highest Common Factor of 918,596,198 using Euclid's algorithm

Highest Common Factor of 918,596,198 is 2

Step 1: Since 918 > 596, we apply the division lemma to 918 and 596, to get

918 = 596 x 1 + 322

Step 2: Since the reminder 596 ≠ 0, we apply division lemma to 322 and 596, to get

596 = 322 x 1 + 274

Step 3: We consider the new divisor 322 and the new remainder 274, and apply the division lemma to get

322 = 274 x 1 + 48

We consider the new divisor 274 and the new remainder 48,and apply the division lemma to get

274 = 48 x 5 + 34

We consider the new divisor 48 and the new remainder 34,and apply the division lemma to get

48 = 34 x 1 + 14

We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get

34 = 14 x 2 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 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 918 and 596 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(48,34) = HCF(274,48) = HCF(322,274) = HCF(596,322) = HCF(918,596) .

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

Step 1: Since 198 > 2, we apply the division lemma to 198 and 2, to get

198 = 2 x 99 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 198 is 2

Notice that 2 = HCF(198,2) .

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Frequently Asked Questions on HCF of 918, 596, 198 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 918, 596, 198?

Answer: HCF of 918, 596, 198 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 918, 596, 198 using Euclid's Algorithm?

Answer: For arbitrary numbers 918, 596, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.