Highest Common Factor of 357, 914, 856 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 357, 914, 856 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 357, 914, 856 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 357, 914, 856 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 357, 914, 856 is 1.

HCF(357, 914, 856) = 1

HCF of 357, 914, 856 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 357, 914, 856 is 1.

Highest Common Factor of 357,914,856 using Euclid's algorithm

Highest Common Factor of 357,914,856 is 1

Step 1: Since 914 > 357, we apply the division lemma to 914 and 357, to get

914 = 357 x 2 + 200

Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 200 and 357, to get

357 = 200 x 1 + 157

Step 3: We consider the new divisor 200 and the new remainder 157, and apply the division lemma to get

200 = 157 x 1 + 43

We consider the new divisor 157 and the new remainder 43,and apply the division lemma to get

157 = 43 x 3 + 28

We consider the new divisor 43 and the new remainder 28,and apply the division lemma to get

43 = 28 x 1 + 15

We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get

28 = 15 x 1 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 357 and 914 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(43,28) = HCF(157,43) = HCF(200,157) = HCF(357,200) = HCF(914,357) .

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

Step 1: Since 856 > 1, we apply the division lemma to 856 and 1, to get

856 = 1 x 856 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 856 is 1

Notice that 1 = HCF(856,1) .

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Frequently Asked Questions on HCF of 357, 914, 856 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 357, 914, 856?

Answer: HCF of 357, 914, 856 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 357, 914, 856 using Euclid's Algorithm?

Answer: For arbitrary numbers 357, 914, 856 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.