Highest Common Factor of 499, 310, 903 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 499, 310, 903 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 499, 310, 903 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 499, 310, 903 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 499, 310, 903 is 1.

HCF(499, 310, 903) = 1

HCF of 499, 310, 903 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 499, 310, 903 is 1.

Highest Common Factor of 499,310,903 using Euclid's algorithm

Highest Common Factor of 499,310,903 is 1

Step 1: Since 499 > 310, we apply the division lemma to 499 and 310, to get

499 = 310 x 1 + 189

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 189 and 310, to get

310 = 189 x 1 + 121

Step 3: We consider the new divisor 189 and the new remainder 121, and apply the division lemma to get

189 = 121 x 1 + 68

We consider the new divisor 121 and the new remainder 68,and apply the division lemma to get

121 = 68 x 1 + 53

We consider the new divisor 68 and the new remainder 53,and apply the division lemma to get

68 = 53 x 1 + 15

We consider the new divisor 53 and the new remainder 15,and apply the division lemma to get

53 = 15 x 3 + 8

We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get

15 = 8 x 1 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 499 and 310 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(53,15) = HCF(68,53) = HCF(121,68) = HCF(189,121) = HCF(310,189) = HCF(499,310) .

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

Step 1: Since 903 > 1, we apply the division lemma to 903 and 1, to get

903 = 1 x 903 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 903 is 1

Notice that 1 = HCF(903,1) .

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Frequently Asked Questions on HCF of 499, 310, 903 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 499, 310, 903?

Answer: HCF of 499, 310, 903 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 499, 310, 903 using Euclid's Algorithm?

Answer: For arbitrary numbers 499, 310, 903 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.