Highest Common Factor of 216, 340, 921 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 216, 340, 921 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 216, 340, 921 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 216, 340, 921 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 216, 340, 921 is 1.

HCF(216, 340, 921) = 1

HCF of 216, 340, 921 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 216, 340, 921 is 1.

Highest Common Factor of 216,340,921 using Euclid's algorithm

Highest Common Factor of 216,340,921 is 1

Step 1: Since 340 > 216, we apply the division lemma to 340 and 216, to get

340 = 216 x 1 + 124

Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 124 and 216, to get

216 = 124 x 1 + 92

Step 3: We consider the new divisor 124 and the new remainder 92, and apply the division lemma to get

124 = 92 x 1 + 32

We consider the new divisor 92 and the new remainder 32,and apply the division lemma to get

92 = 32 x 2 + 28

We consider the new divisor 32 and the new remainder 28,and apply the division lemma to get

32 = 28 x 1 + 4

We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get

28 = 4 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 216 and 340 is 4

Notice that 4 = HCF(28,4) = HCF(32,28) = HCF(92,32) = HCF(124,92) = HCF(216,124) = HCF(340,216) .

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

Step 1: Since 921 > 4, we apply the division lemma to 921 and 4, to get

921 = 4 x 230 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 921 is 1

Notice that 1 = HCF(4,1) = HCF(921,4) .

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Frequently Asked Questions on HCF of 216, 340, 921 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 216, 340, 921?

Answer: HCF of 216, 340, 921 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 216, 340, 921 using Euclid's Algorithm?

Answer: For arbitrary numbers 216, 340, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.