Highest Common Factor of 733, 466, 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 733, 466, 198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 733, 466, 198 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 733, 466, 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 733, 466, 198 is 1.

HCF(733, 466, 198) = 1

HCF of 733, 466, 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 733, 466, 198 is 1.

Highest Common Factor of 733,466,198 using Euclid's algorithm

Highest Common Factor of 733,466,198 is 1

Step 1: Since 733 > 466, we apply the division lemma to 733 and 466, to get

733 = 466 x 1 + 267

Step 2: Since the reminder 466 ≠ 0, we apply division lemma to 267 and 466, to get

466 = 267 x 1 + 199

Step 3: We consider the new divisor 267 and the new remainder 199, and apply the division lemma to get

267 = 199 x 1 + 68

We consider the new divisor 199 and the new remainder 68,and apply the division lemma to get

199 = 68 x 2 + 63

We consider the new divisor 68 and the new remainder 63,and apply the division lemma to get

68 = 63 x 1 + 5

We consider the new divisor 63 and the new remainder 5,and apply the division lemma to get

63 = 5 x 12 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 733 and 466 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(63,5) = HCF(68,63) = HCF(199,68) = HCF(267,199) = HCF(466,267) = HCF(733,466) .

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

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

198 = 1 x 198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 198 is 1

Notice that 1 = HCF(198,1) .

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Frequently Asked Questions on HCF of 733, 466, 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 733, 466, 198?

Answer: HCF of 733, 466, 198 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 733, 466, 198 using Euclid's Algorithm?

Answer: For arbitrary numbers 733, 466, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.