Highest Common Factor of 609, 986, 158 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 609, 986, 158 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 609, 986, 158 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 609, 986, 158 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 609, 986, 158 is 1.

HCF(609, 986, 158) = 1

HCF of 609, 986, 158 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 609, 986, 158 is 1.

Highest Common Factor of 609,986,158 using Euclid's algorithm

Highest Common Factor of 609,986,158 is 1

Step 1: Since 986 > 609, we apply the division lemma to 986 and 609, to get

986 = 609 x 1 + 377

Step 2: Since the reminder 609 ≠ 0, we apply division lemma to 377 and 609, to get

609 = 377 x 1 + 232

Step 3: We consider the new divisor 377 and the new remainder 232, and apply the division lemma to get

377 = 232 x 1 + 145

We consider the new divisor 232 and the new remainder 145,and apply the division lemma to get

232 = 145 x 1 + 87

We consider the new divisor 145 and the new remainder 87,and apply the division lemma to get

145 = 87 x 1 + 58

We consider the new divisor 87 and the new remainder 58,and apply the division lemma to get

87 = 58 x 1 + 29

We consider the new divisor 58 and the new remainder 29,and apply the division lemma to get

58 = 29 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 609 and 986 is 29

Notice that 29 = HCF(58,29) = HCF(87,58) = HCF(145,87) = HCF(232,145) = HCF(377,232) = HCF(609,377) = HCF(986,609) .

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

Step 1: Since 158 > 29, we apply the division lemma to 158 and 29, to get

158 = 29 x 5 + 13

Step 2: Since the reminder 29 ≠ 0, we apply division lemma to 13 and 29, to get

29 = 13 x 2 + 3

Step 3: We consider the new divisor 13 and the new remainder 3, and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 29 and 158 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(158,29) .

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Frequently Asked Questions on HCF of 609, 986, 158 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 609, 986, 158?

Answer: HCF of 609, 986, 158 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 609, 986, 158 using Euclid's Algorithm?

Answer: For arbitrary numbers 609, 986, 158 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.