Highest Common Factor of 163, 222, 409 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 163, 222, 409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 163, 222, 409 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 163, 222, 409 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 163, 222, 409 is 1.

HCF(163, 222, 409) = 1

HCF of 163, 222, 409 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 163, 222, 409 is 1.

Highest Common Factor of 163,222,409 using Euclid's algorithm

Highest Common Factor of 163,222,409 is 1

Step 1: Since 222 > 163, we apply the division lemma to 222 and 163, to get

222 = 163 x 1 + 59

Step 2: Since the reminder 163 ≠ 0, we apply division lemma to 59 and 163, to get

163 = 59 x 2 + 45

Step 3: We consider the new divisor 59 and the new remainder 45, and apply the division lemma to get

59 = 45 x 1 + 14

We consider the new divisor 45 and the new remainder 14,and apply the division lemma to get

45 = 14 x 3 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 163 and 222 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(45,14) = HCF(59,45) = HCF(163,59) = HCF(222,163) .

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

Step 1: Since 409 > 1, we apply the division lemma to 409 and 1, to get

409 = 1 x 409 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 409 is 1

Notice that 1 = HCF(409,1) .

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Frequently Asked Questions on HCF of 163, 222, 409 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 163, 222, 409?

Answer: HCF of 163, 222, 409 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 163, 222, 409 using Euclid's Algorithm?

Answer: For arbitrary numbers 163, 222, 409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.