Highest Common Factor of 986, 364, 219 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 986, 364, 219 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 986, 364, 219 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 986, 364, 219 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 986, 364, 219 is 1.

HCF(986, 364, 219) = 1

HCF of 986, 364, 219 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 986, 364, 219 is 1.

Highest Common Factor of 986,364,219 using Euclid's algorithm

Highest Common Factor of 986,364,219 is 1

Step 1: Since 986 > 364, we apply the division lemma to 986 and 364, to get

986 = 364 x 2 + 258

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 258 and 364, to get

364 = 258 x 1 + 106

Step 3: We consider the new divisor 258 and the new remainder 106, and apply the division lemma to get

258 = 106 x 2 + 46

We consider the new divisor 106 and the new remainder 46,and apply the division lemma to get

106 = 46 x 2 + 14

We consider the new divisor 46 and the new remainder 14,and apply the division lemma to get

46 = 14 x 3 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 986 and 364 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(46,14) = HCF(106,46) = HCF(258,106) = HCF(364,258) = HCF(986,364) .

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

Step 1: Since 219 > 2, we apply the division lemma to 219 and 2, to get

219 = 2 x 109 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 219 is 1

Notice that 1 = HCF(2,1) = HCF(219,2) .

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Frequently Asked Questions on HCF of 986, 364, 219 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 986, 364, 219?

Answer: HCF of 986, 364, 219 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 986, 364, 219 using Euclid's Algorithm?

Answer: For arbitrary numbers 986, 364, 219 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.