Highest Common Factor of 783, 215, 288 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 783, 215, 288 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 783, 215, 288 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 783, 215, 288 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 783, 215, 288 is 1.

HCF(783, 215, 288) = 1

HCF of 783, 215, 288 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 783, 215, 288 is 1.

Highest Common Factor of 783,215,288 using Euclid's algorithm

Highest Common Factor of 783,215,288 is 1

Step 1: Since 783 > 215, we apply the division lemma to 783 and 215, to get

783 = 215 x 3 + 138

Step 2: Since the reminder 215 ≠ 0, we apply division lemma to 138 and 215, to get

215 = 138 x 1 + 77

Step 3: We consider the new divisor 138 and the new remainder 77, and apply the division lemma to get

138 = 77 x 1 + 61

We consider the new divisor 77 and the new remainder 61,and apply the division lemma to get

77 = 61 x 1 + 16

We consider the new divisor 61 and the new remainder 16,and apply the division lemma to get

61 = 16 x 3 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

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 783 and 215 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(61,16) = HCF(77,61) = HCF(138,77) = HCF(215,138) = HCF(783,215) .

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

Step 1: Since 288 > 1, we apply the division lemma to 288 and 1, to get

288 = 1 x 288 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 288 is 1

Notice that 1 = HCF(288,1) .

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Frequently Asked Questions on HCF of 783, 215, 288 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 783, 215, 288?

Answer: HCF of 783, 215, 288 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 783, 215, 288 using Euclid's Algorithm?

Answer: For arbitrary numbers 783, 215, 288 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.