Highest Common Factor of 662, 417, 913 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 662, 417, 913 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 662, 417, 913 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 662, 417, 913 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 662, 417, 913 is 1.

HCF(662, 417, 913) = 1

HCF of 662, 417, 913 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 662, 417, 913 is 1.

Highest Common Factor of 662,417,913 using Euclid's algorithm

Highest Common Factor of 662,417,913 is 1

Step 1: Since 662 > 417, we apply the division lemma to 662 and 417, to get

662 = 417 x 1 + 245

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 245 and 417, to get

417 = 245 x 1 + 172

Step 3: We consider the new divisor 245 and the new remainder 172, and apply the division lemma to get

245 = 172 x 1 + 73

We consider the new divisor 172 and the new remainder 73,and apply the division lemma to get

172 = 73 x 2 + 26

We consider the new divisor 73 and the new remainder 26,and apply the division lemma to get

73 = 26 x 2 + 21

We consider the new divisor 26 and the new remainder 21,and apply the division lemma to get

26 = 21 x 1 + 5

We consider the new divisor 21 and the new remainder 5,and apply the division lemma to get

21 = 5 x 4 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 662 and 417 is 1

Notice that 1 = HCF(5,1) = HCF(21,5) = HCF(26,21) = HCF(73,26) = HCF(172,73) = HCF(245,172) = HCF(417,245) = HCF(662,417) .

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

Step 1: Since 913 > 1, we apply the division lemma to 913 and 1, to get

913 = 1 x 913 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 913 is 1

Notice that 1 = HCF(913,1) .

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Frequently Asked Questions on HCF of 662, 417, 913 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 662, 417, 913?

Answer: HCF of 662, 417, 913 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 662, 417, 913 using Euclid's Algorithm?

Answer: For arbitrary numbers 662, 417, 913 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.