Highest Common Factor of 84, 219, 790 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 84, 219, 790 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 84, 219, 790 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 84, 219, 790 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 84, 219, 790 is 1.

HCF(84, 219, 790) = 1

HCF of 84, 219, 790 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 84, 219, 790 is 1.

Highest Common Factor of 84,219,790 using Euclid's algorithm

Highest Common Factor of 84,219,790 is 1

Step 1: Since 219 > 84, we apply the division lemma to 219 and 84, to get

219 = 84 x 2 + 51

Step 2: Since the reminder 84 ≠ 0, we apply division lemma to 51 and 84, to get

84 = 51 x 1 + 33

Step 3: We consider the new divisor 51 and the new remainder 33, and apply the division lemma to get

51 = 33 x 1 + 18

We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get

33 = 18 x 1 + 15

We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get

18 = 15 x 1 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 84 and 219 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) = HCF(84,51) = HCF(219,84) .

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

Step 1: Since 790 > 3, we apply the division lemma to 790 and 3, to get

790 = 3 x 263 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 790 is 1

Notice that 1 = HCF(3,1) = HCF(790,3) .

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Frequently Asked Questions on HCF of 84, 219, 790 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 84, 219, 790?

Answer: HCF of 84, 219, 790 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 84, 219, 790 using Euclid's Algorithm?

Answer: For arbitrary numbers 84, 219, 790 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.