Highest Common Factor of 417, 257, 11 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 417, 257, 11 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 417, 257, 11 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 417, 257, 11 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 417, 257, 11 is 1.

HCF(417, 257, 11) = 1

HCF of 417, 257, 11 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 417, 257, 11 is 1.

Highest Common Factor of 417,257,11 using Euclid's algorithm

Highest Common Factor of 417,257,11 is 1

Step 1: Since 417 > 257, we apply the division lemma to 417 and 257, to get

417 = 257 x 1 + 160

Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 160 and 257, to get

257 = 160 x 1 + 97

Step 3: We consider the new divisor 160 and the new remainder 97, and apply the division lemma to get

160 = 97 x 1 + 63

We consider the new divisor 97 and the new remainder 63,and apply the division lemma to get

97 = 63 x 1 + 34

We consider the new divisor 63 and the new remainder 34,and apply the division lemma to get

63 = 34 x 1 + 29

We consider the new divisor 34 and the new remainder 29,and apply the division lemma to get

34 = 29 x 1 + 5

We consider the new divisor 29 and the new remainder 5,and apply the division lemma to get

29 = 5 x 5 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 417 and 257 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(29,5) = HCF(34,29) = HCF(63,34) = HCF(97,63) = HCF(160,97) = HCF(257,160) = HCF(417,257) .

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

Step 1: Since 11 > 1, we apply the division lemma to 11 and 1, to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 11 is 1

Notice that 1 = HCF(11,1) .

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Frequently Asked Questions on HCF of 417, 257, 11 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 417, 257, 11?

Answer: HCF of 417, 257, 11 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 417, 257, 11 using Euclid's Algorithm?

Answer: For arbitrary numbers 417, 257, 11 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.