Highest Common Factor of 848, 321, 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 848, 321, 219 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 848, 321, 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 848, 321, 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 848, 321, 219 is 1.

HCF(848, 321, 219) = 1

HCF of 848, 321, 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 848, 321, 219 is 1.

Highest Common Factor of 848,321,219 using Euclid's algorithm

Highest Common Factor of 848,321,219 is 1

Step 1: Since 848 > 321, we apply the division lemma to 848 and 321, to get

848 = 321 x 2 + 206

Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 206 and 321, to get

321 = 206 x 1 + 115

Step 3: We consider the new divisor 206 and the new remainder 115, and apply the division lemma to get

206 = 115 x 1 + 91

We consider the new divisor 115 and the new remainder 91,and apply the division lemma to get

115 = 91 x 1 + 24

We consider the new divisor 91 and the new remainder 24,and apply the division lemma to get

91 = 24 x 3 + 19

We consider the new divisor 24 and the new remainder 19,and apply the division lemma to get

24 = 19 x 1 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

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 848 and 321 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(91,24) = HCF(115,91) = HCF(206,115) = HCF(321,206) = HCF(848,321) .

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

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

219 = 1 x 219 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 219 is 1

Notice that 1 = HCF(219,1) .

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Frequently Asked Questions on HCF of 848, 321, 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 848, 321, 219?

Answer: HCF of 848, 321, 219 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 848, 321, 219 using Euclid's Algorithm?

Answer: For arbitrary numbers 848, 321, 219 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.