Highest Common Factor of 412, 661, 575 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, 661, 575 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 412, 661, 575 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, 661, 575 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, 661, 575 is 1.

HCF(412, 661, 575) = 1

HCF of 412, 661, 575 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, 661, 575 is 1.

Highest Common Factor of 412,661,575 using Euclid's algorithm

Highest Common Factor of 412,661,575 is 1

Step 1: Since 661 > 412, we apply the division lemma to 661 and 412, to get

661 = 412 x 1 + 249

Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 249 and 412, to get

412 = 249 x 1 + 163

Step 3: We consider the new divisor 249 and the new remainder 163, and apply the division lemma to get

249 = 163 x 1 + 86

We consider the new divisor 163 and the new remainder 86,and apply the division lemma to get

163 = 86 x 1 + 77

We consider the new divisor 86 and the new remainder 77,and apply the division lemma to get

86 = 77 x 1 + 9

We consider the new divisor 77 and the new remainder 9,and apply the division lemma to get

77 = 9 x 8 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 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 412 and 661 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(77,9) = HCF(86,77) = HCF(163,86) = HCF(249,163) = HCF(412,249) = HCF(661,412) .

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

Step 1: Since 575 > 1, we apply the division lemma to 575 and 1, to get

575 = 1 x 575 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 575 is 1

Notice that 1 = HCF(575,1) .

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Frequently Asked Questions on HCF of 412, 661, 575 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, 661, 575?

Answer: HCF of 412, 661, 575 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 412, 661, 575 using Euclid's Algorithm?

Answer: For arbitrary numbers 412, 661, 575 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.