Highest Common Factor of 229, 409, 998 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 229, 409, 998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 229, 409, 998 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 229, 409, 998 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 229, 409, 998 is 1.

HCF(229, 409, 998) = 1

HCF of 229, 409, 998 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 229, 409, 998 is 1.

Highest Common Factor of 229,409,998 using Euclid's algorithm

Highest Common Factor of 229,409,998 is 1

Step 1: Since 409 > 229, we apply the division lemma to 409 and 229, to get

409 = 229 x 1 + 180

Step 2: Since the reminder 229 ≠ 0, we apply division lemma to 180 and 229, to get

229 = 180 x 1 + 49

Step 3: We consider the new divisor 180 and the new remainder 49, and apply the division lemma to get

180 = 49 x 3 + 33

We consider the new divisor 49 and the new remainder 33,and apply the division lemma to get

49 = 33 x 1 + 16

We consider the new divisor 33 and the new remainder 16,and apply the division lemma to get

33 = 16 x 2 + 1

We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get

16 = 1 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 229 and 409 is 1

Notice that 1 = HCF(16,1) = HCF(33,16) = HCF(49,33) = HCF(180,49) = HCF(229,180) = HCF(409,229) .

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

Step 1: Since 998 > 1, we apply the division lemma to 998 and 1, to get

998 = 1 x 998 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 998 is 1

Notice that 1 = HCF(998,1) .

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Frequently Asked Questions on HCF of 229, 409, 998 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 229, 409, 998?

Answer: HCF of 229, 409, 998 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 229, 409, 998 using Euclid's Algorithm?

Answer: For arbitrary numbers 229, 409, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.