Highest Common Factor of 189, 306, 986 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 189, 306, 986 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 189, 306, 986 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 189, 306, 986 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 189, 306, 986 is 1.

HCF(189, 306, 986) = 1

HCF of 189, 306, 986 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 189, 306, 986 is 1.

Highest Common Factor of 189,306,986 using Euclid's algorithm

Highest Common Factor of 189,306,986 is 1

Step 1: Since 306 > 189, we apply the division lemma to 306 and 189, to get

306 = 189 x 1 + 117

Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 117 and 189, to get

189 = 117 x 1 + 72

Step 3: We consider the new divisor 117 and the new remainder 72, and apply the division lemma to get

117 = 72 x 1 + 45

We consider the new divisor 72 and the new remainder 45,and apply the division lemma to get

72 = 45 x 1 + 27

We consider the new divisor 45 and the new remainder 27,and apply the division lemma to get

45 = 27 x 1 + 18

We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get

27 = 18 x 1 + 9

We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 189 and 306 is 9

Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(45,27) = HCF(72,45) = HCF(117,72) = HCF(189,117) = HCF(306,189) .

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

Step 1: Since 986 > 9, we apply the division lemma to 986 and 9, to get

986 = 9 x 109 + 5

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 5 and 9, to get

9 = 5 x 1 + 4

Step 3: We consider the new divisor 5 and the new remainder 4, and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 986 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(986,9) .

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Frequently Asked Questions on HCF of 189, 306, 986 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 189, 306, 986?

Answer: HCF of 189, 306, 986 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 189, 306, 986 using Euclid's Algorithm?

Answer: For arbitrary numbers 189, 306, 986 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.