Highest Common Factor of 497, 305, 313 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 497, 305, 313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 497, 305, 313 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 497, 305, 313 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 497, 305, 313 is 1.

HCF(497, 305, 313) = 1

HCF of 497, 305, 313 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 497, 305, 313 is 1.

Highest Common Factor of 497,305,313 using Euclid's algorithm

Highest Common Factor of 497,305,313 is 1

Step 1: Since 497 > 305, we apply the division lemma to 497 and 305, to get

497 = 305 x 1 + 192

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 192 and 305, to get

305 = 192 x 1 + 113

Step 3: We consider the new divisor 192 and the new remainder 113, and apply the division lemma to get

192 = 113 x 1 + 79

We consider the new divisor 113 and the new remainder 79,and apply the division lemma to get

113 = 79 x 1 + 34

We consider the new divisor 79 and the new remainder 34,and apply the division lemma to get

79 = 34 x 2 + 11

We consider the new divisor 34 and the new remainder 11,and apply the division lemma to get

34 = 11 x 3 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma 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 497 and 305 is 1

Notice that 1 = HCF(11,1) = HCF(34,11) = HCF(79,34) = HCF(113,79) = HCF(192,113) = HCF(305,192) = HCF(497,305) .

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

Step 1: Since 313 > 1, we apply the division lemma to 313 and 1, to get

313 = 1 x 313 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 313 is 1

Notice that 1 = HCF(313,1) .

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Frequently Asked Questions on HCF of 497, 305, 313 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 497, 305, 313?

Answer: HCF of 497, 305, 313 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 497, 305, 313 using Euclid's Algorithm?

Answer: For arbitrary numbers 497, 305, 313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.