Highest Common Factor of 342, 860, 340 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 342, 860, 340 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 342, 860, 340 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 342, 860, 340 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 342, 860, 340 is 2.

HCF(342, 860, 340) = 2

HCF of 342, 860, 340 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 342, 860, 340 is 2.

Highest Common Factor of 342,860,340 using Euclid's algorithm

Highest Common Factor of 342,860,340 is 2

Step 1: Since 860 > 342, we apply the division lemma to 860 and 342, to get

860 = 342 x 2 + 176

Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 176 and 342, to get

342 = 176 x 1 + 166

Step 3: We consider the new divisor 176 and the new remainder 166, and apply the division lemma to get

176 = 166 x 1 + 10

We consider the new divisor 166 and the new remainder 10,and apply the division lemma to get

166 = 10 x 16 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 342 and 860 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(166,10) = HCF(176,166) = HCF(342,176) = HCF(860,342) .

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

Step 1: Since 340 > 2, we apply the division lemma to 340 and 2, to get

340 = 2 x 170 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 340 is 2

Notice that 2 = HCF(340,2) .

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Frequently Asked Questions on HCF of 342, 860, 340 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 342, 860, 340?

Answer: HCF of 342, 860, 340 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 342, 860, 340 using Euclid's Algorithm?

Answer: For arbitrary numbers 342, 860, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.