Highest Common Factor of 7204, 3343, 20519 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 7204, 3343, 20519 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7204, 3343, 20519 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 7204, 3343, 20519 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 7204, 3343, 20519 is 1.

HCF(7204, 3343, 20519) = 1

HCF of 7204, 3343, 20519 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 7204, 3343, 20519 is 1.

Highest Common Factor of 7204,3343,20519 using Euclid's algorithm

Highest Common Factor of 7204,3343,20519 is 1

Step 1: Since 7204 > 3343, we apply the division lemma to 7204 and 3343, to get

7204 = 3343 x 2 + 518

Step 2: Since the reminder 3343 ≠ 0, we apply division lemma to 518 and 3343, to get

3343 = 518 x 6 + 235

Step 3: We consider the new divisor 518 and the new remainder 235, and apply the division lemma to get

518 = 235 x 2 + 48

We consider the new divisor 235 and the new remainder 48,and apply the division lemma to get

235 = 48 x 4 + 43

We consider the new divisor 48 and the new remainder 43,and apply the division lemma to get

48 = 43 x 1 + 5

We consider the new divisor 43 and the new remainder 5,and apply the division lemma to get

43 = 5 x 8 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7204 and 3343 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(43,5) = HCF(48,43) = HCF(235,48) = HCF(518,235) = HCF(3343,518) = HCF(7204,3343) .

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

Step 1: Since 20519 > 1, we apply the division lemma to 20519 and 1, to get

20519 = 1 x 20519 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20519 is 1

Notice that 1 = HCF(20519,1) .

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Frequently Asked Questions on HCF of 7204, 3343, 20519 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 7204, 3343, 20519?

Answer: HCF of 7204, 3343, 20519 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7204, 3343, 20519 using Euclid's Algorithm?

Answer: For arbitrary numbers 7204, 3343, 20519 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.