Highest Common Factor of 219, 299, 838 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 219, 299, 838 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 219, 299, 838 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 219, 299, 838 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 219, 299, 838 is 1.

HCF(219, 299, 838) = 1

HCF of 219, 299, 838 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 219, 299, 838 is 1.

Highest Common Factor of 219,299,838 using Euclid's algorithm

Highest Common Factor of 219,299,838 is 1

Step 1: Since 299 > 219, we apply the division lemma to 299 and 219, to get

299 = 219 x 1 + 80

Step 2: Since the reminder 219 ≠ 0, we apply division lemma to 80 and 219, to get

219 = 80 x 2 + 59

Step 3: We consider the new divisor 80 and the new remainder 59, and apply the division lemma to get

80 = 59 x 1 + 21

We consider the new divisor 59 and the new remainder 21,and apply the division lemma to get

59 = 21 x 2 + 17

We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get

21 = 17 x 1 + 4

We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get

17 = 4 x 4 + 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 219 and 299 is 1

Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(59,21) = HCF(80,59) = HCF(219,80) = HCF(299,219) .

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

Step 1: Since 838 > 1, we apply the division lemma to 838 and 1, to get

838 = 1 x 838 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 838 is 1

Notice that 1 = HCF(838,1) .

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Frequently Asked Questions on HCF of 219, 299, 838 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 219, 299, 838?

Answer: HCF of 219, 299, 838 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 219, 299, 838 using Euclid's Algorithm?

Answer: For arbitrary numbers 219, 299, 838 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.