Highest Common Factor of 499, 193, 310, 38 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, 193, 310, 38 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 499, 193, 310, 38 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, 193, 310, 38 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, 193, 310, 38 is 1.

HCF(499, 193, 310, 38) = 1

HCF of 499, 193, 310, 38 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, 193, 310, 38 is 1.

Highest Common Factor of 499,193,310,38 using Euclid's algorithm

Highest Common Factor of 499,193,310,38 is 1

Step 1: Since 499 > 193, we apply the division lemma to 499 and 193, to get

499 = 193 x 2 + 113

Step 2: Since the reminder 193 ≠ 0, we apply division lemma to 113 and 193, to get

193 = 113 x 1 + 80

Step 3: We consider the new divisor 113 and the new remainder 80, and apply the division lemma to get

113 = 80 x 1 + 33

We consider the new divisor 80 and the new remainder 33,and apply the division lemma to get

80 = 33 x 2 + 14

We consider the new divisor 33 and the new remainder 14,and apply the division lemma to get

33 = 14 x 2 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 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 499 and 193 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(33,14) = HCF(80,33) = HCF(113,80) = HCF(193,113) = HCF(499,193) .

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

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

310 = 1 x 310 + 0

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

Notice that 1 = HCF(310,1) .

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

Step 1: Since 38 > 1, we apply the division lemma to 38 and 1, to get

38 = 1 x 38 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 38 is 1

Notice that 1 = HCF(38,1) .

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Frequently Asked Questions on HCF of 499, 193, 310, 38 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, 193, 310, 38?

Answer: HCF of 499, 193, 310, 38 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 499, 193, 310, 38 using Euclid's Algorithm?

Answer: For arbitrary numbers 499, 193, 310, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.