Highest Common Factor of 420, 560, 193 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 420, 560, 193 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 560, 193 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 420, 560, 193 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 420, 560, 193 is 1.

HCF(420, 560, 193) = 1

HCF of 420, 560, 193 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 420, 560, 193 is 1.

Highest Common Factor of 420,560,193 using Euclid's algorithm

Highest Common Factor of 420,560,193 is 1

Step 1: Since 560 > 420, we apply the division lemma to 560 and 420, to get

560 = 420 x 1 + 140

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 140 and 420, to get

420 = 140 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 140, the HCF of 420 and 560 is 140

Notice that 140 = HCF(420,140) = HCF(560,420) .

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

Step 1: Since 193 > 140, we apply the division lemma to 193 and 140, to get

193 = 140 x 1 + 53

Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 53 and 140, to get

140 = 53 x 2 + 34

Step 3: We consider the new divisor 53 and the new remainder 34, and apply the division lemma to get

53 = 34 x 1 + 19

We consider the new divisor 34 and the new remainder 19,and apply the division lemma to get

34 = 19 x 1 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 140 and 193 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(34,19) = HCF(53,34) = HCF(140,53) = HCF(193,140) .

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Frequently Asked Questions on HCF of 420, 560, 193 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 420, 560, 193?

Answer: HCF of 420, 560, 193 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 560, 193 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 560, 193 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.