Highest Common Factor of 993, 358, 223 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 993, 358, 223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 993, 358, 223 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 993, 358, 223 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 993, 358, 223 is 1.

HCF(993, 358, 223) = 1

HCF of 993, 358, 223 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 993, 358, 223 is 1.

Highest Common Factor of 993,358,223 using Euclid's algorithm

Highest Common Factor of 993,358,223 is 1

Step 1: Since 993 > 358, we apply the division lemma to 993 and 358, to get

993 = 358 x 2 + 277

Step 2: Since the reminder 358 ≠ 0, we apply division lemma to 277 and 358, to get

358 = 277 x 1 + 81

Step 3: We consider the new divisor 277 and the new remainder 81, and apply the division lemma to get

277 = 81 x 3 + 34

We consider the new divisor 81 and the new remainder 34,and apply the division lemma to get

81 = 34 x 2 + 13

We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get

34 = 13 x 2 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 993 and 358 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(81,34) = HCF(277,81) = HCF(358,277) = HCF(993,358) .

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

Step 1: Since 223 > 1, we apply the division lemma to 223 and 1, to get

223 = 1 x 223 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 223 is 1

Notice that 1 = HCF(223,1) .

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Frequently Asked Questions on HCF of 993, 358, 223 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 993, 358, 223?

Answer: HCF of 993, 358, 223 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 993, 358, 223 using Euclid's Algorithm?

Answer: For arbitrary numbers 993, 358, 223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.