Highest Common Factor of 998, 605, 167 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, 605, 167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 998, 605, 167 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, 605, 167 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, 605, 167 is 1.

HCF(998, 605, 167) = 1

HCF of 998, 605, 167 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, 605, 167 is 1.

Highest Common Factor of 998,605,167 using Euclid's algorithm

Highest Common Factor of 998,605,167 is 1

Step 1: Since 998 > 605, we apply the division lemma to 998 and 605, to get

998 = 605 x 1 + 393

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 393 and 605, to get

605 = 393 x 1 + 212

Step 3: We consider the new divisor 393 and the new remainder 212, and apply the division lemma to get

393 = 212 x 1 + 181

We consider the new divisor 212 and the new remainder 181,and apply the division lemma to get

212 = 181 x 1 + 31

We consider the new divisor 181 and the new remainder 31,and apply the division lemma to get

181 = 31 x 5 + 26

We consider the new divisor 31 and the new remainder 26,and apply the division lemma to get

31 = 26 x 1 + 5

We consider the new divisor 26 and the new remainder 5,and apply the division lemma to get

26 = 5 x 5 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 998 and 605 is 1

Notice that 1 = HCF(5,1) = HCF(26,5) = HCF(31,26) = HCF(181,31) = HCF(212,181) = HCF(393,212) = HCF(605,393) = HCF(998,605) .

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

Step 1: Since 167 > 1, we apply the division lemma to 167 and 1, to get

167 = 1 x 167 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 167 is 1

Notice that 1 = HCF(167,1) .

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Frequently Asked Questions on HCF of 998, 605, 167 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, 605, 167?

Answer: HCF of 998, 605, 167 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 998, 605, 167 using Euclid's Algorithm?

Answer: For arbitrary numbers 998, 605, 167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.