Highest Common Factor of 857, 545, 768 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 857, 545, 768 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 857, 545, 768 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 857, 545, 768 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 857, 545, 768 is 1.

HCF(857, 545, 768) = 1

HCF of 857, 545, 768 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 857, 545, 768 is 1.

Highest Common Factor of 857,545,768 using Euclid's algorithm

Highest Common Factor of 857,545,768 is 1

Step 1: Since 857 > 545, we apply the division lemma to 857 and 545, to get

857 = 545 x 1 + 312

Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 312 and 545, to get

545 = 312 x 1 + 233

Step 3: We consider the new divisor 312 and the new remainder 233, and apply the division lemma to get

312 = 233 x 1 + 79

We consider the new divisor 233 and the new remainder 79,and apply the division lemma to get

233 = 79 x 2 + 75

We consider the new divisor 79 and the new remainder 75,and apply the division lemma to get

79 = 75 x 1 + 4

We consider the new divisor 75 and the new remainder 4,and apply the division lemma to get

75 = 4 x 18 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 857 and 545 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(75,4) = HCF(79,75) = HCF(233,79) = HCF(312,233) = HCF(545,312) = HCF(857,545) .

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

Step 1: Since 768 > 1, we apply the division lemma to 768 and 1, to get

768 = 1 x 768 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 768 is 1

Notice that 1 = HCF(768,1) .

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Frequently Asked Questions on HCF of 857, 545, 768 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 857, 545, 768?

Answer: HCF of 857, 545, 768 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 857, 545, 768 using Euclid's Algorithm?

Answer: For arbitrary numbers 857, 545, 768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.