Highest Common Factor of 298, 786, 34 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 298, 786, 34 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 298, 786, 34 is 2 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 298, 786, 34 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 298, 786, 34 is 2.

HCF(298, 786, 34) = 2

HCF of 298, 786, 34 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 298, 786, 34 is 2.

Highest Common Factor of 298,786,34 using Euclid's algorithm

Highest Common Factor of 298,786,34 is 2

Step 1: Since 786 > 298, we apply the division lemma to 786 and 298, to get

786 = 298 x 2 + 190

Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 190 and 298, to get

298 = 190 x 1 + 108

Step 3: We consider the new divisor 190 and the new remainder 108, and apply the division lemma to get

190 = 108 x 1 + 82

We consider the new divisor 108 and the new remainder 82,and apply the division lemma to get

108 = 82 x 1 + 26

We consider the new divisor 82 and the new remainder 26,and apply the division lemma to get

82 = 26 x 3 + 4

We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get

26 = 4 x 6 + 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 298 and 786 is 2

Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(82,26) = HCF(108,82) = HCF(190,108) = HCF(298,190) = HCF(786,298) .

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

Step 1: Since 34 > 2, we apply the division lemma to 34 and 2, to get

34 = 2 x 17 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 34 is 2

Notice that 2 = HCF(34,2) .

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Frequently Asked Questions on HCF of 298, 786, 34 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 298, 786, 34?

Answer: HCF of 298, 786, 34 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 298, 786, 34 using Euclid's Algorithm?

Answer: For arbitrary numbers 298, 786, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.