Highest Common Factor of 412, 741, 560 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 412, 741, 560 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 412, 741, 560 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 412, 741, 560 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 412, 741, 560 is 1.

HCF(412, 741, 560) = 1

HCF of 412, 741, 560 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 412, 741, 560 is 1.

Highest Common Factor of 412,741,560 using Euclid's algorithm

Highest Common Factor of 412,741,560 is 1

Step 1: Since 741 > 412, we apply the division lemma to 741 and 412, to get

741 = 412 x 1 + 329

Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 329 and 412, to get

412 = 329 x 1 + 83

Step 3: We consider the new divisor 329 and the new remainder 83, and apply the division lemma to get

329 = 83 x 3 + 80

We consider the new divisor 83 and the new remainder 80,and apply the division lemma to get

83 = 80 x 1 + 3

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

80 = 3 x 26 + 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 412 and 741 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(80,3) = HCF(83,80) = HCF(329,83) = HCF(412,329) = HCF(741,412) .

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

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

560 = 1 x 560 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 560 is 1

Notice that 1 = HCF(560,1) .

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Frequently Asked Questions on HCF of 412, 741, 560 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 412, 741, 560?

Answer: HCF of 412, 741, 560 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 412, 741, 560 using Euclid's Algorithm?

Answer: For arbitrary numbers 412, 741, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.