Highest Common Factor of 168, 412, 163 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 168, 412, 163 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 168, 412, 163 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 168, 412, 163 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 168, 412, 163 is 1.

HCF(168, 412, 163) = 1

HCF of 168, 412, 163 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 168, 412, 163 is 1.

Highest Common Factor of 168,412,163 using Euclid's algorithm

Highest Common Factor of 168,412,163 is 1

Step 1: Since 412 > 168, we apply the division lemma to 412 and 168, to get

412 = 168 x 2 + 76

Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 76 and 168, to get

168 = 76 x 2 + 16

Step 3: We consider the new divisor 76 and the new remainder 16, and apply the division lemma to get

76 = 16 x 4 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 168 and 412 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(76,16) = HCF(168,76) = HCF(412,168) .

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

Step 1: Since 163 > 4, we apply the division lemma to 163 and 4, to get

163 = 4 x 40 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 163 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(163,4) .

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Frequently Asked Questions on HCF of 168, 412, 163 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 168, 412, 163?

Answer: HCF of 168, 412, 163 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 168, 412, 163 using Euclid's Algorithm?

Answer: For arbitrary numbers 168, 412, 163 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.