Highest Common Factor of 616, 340, 243 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 616, 340, 243 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 616, 340, 243 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 616, 340, 243 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 616, 340, 243 is 1.

HCF(616, 340, 243) = 1

HCF of 616, 340, 243 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 616, 340, 243 is 1.

Highest Common Factor of 616,340,243 using Euclid's algorithm

Highest Common Factor of 616,340,243 is 1

Step 1: Since 616 > 340, we apply the division lemma to 616 and 340, to get

616 = 340 x 1 + 276

Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 276 and 340, to get

340 = 276 x 1 + 64

Step 3: We consider the new divisor 276 and the new remainder 64, and apply the division lemma to get

276 = 64 x 4 + 20

We consider the new divisor 64 and the new remainder 20,and apply the division lemma to get

64 = 20 x 3 + 4

We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 616 and 340 is 4

Notice that 4 = HCF(20,4) = HCF(64,20) = HCF(276,64) = HCF(340,276) = HCF(616,340) .

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

Step 1: Since 243 > 4, we apply the division lemma to 243 and 4, to get

243 = 4 x 60 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 4 and 243 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(243,4) .

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Frequently Asked Questions on HCF of 616, 340, 243 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 616, 340, 243?

Answer: HCF of 616, 340, 243 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 616, 340, 243 using Euclid's Algorithm?

Answer: For arbitrary numbers 616, 340, 243 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.