Highest Common Factor of 988, 343, 224 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 988, 343, 224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 988, 343, 224 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 988, 343, 224 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 988, 343, 224 is 1.

HCF(988, 343, 224) = 1

HCF of 988, 343, 224 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 988, 343, 224 is 1.

Highest Common Factor of 988,343,224 using Euclid's algorithm

Highest Common Factor of 988,343,224 is 1

Step 1: Since 988 > 343, we apply the division lemma to 988 and 343, to get

988 = 343 x 2 + 302

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 302 and 343, to get

343 = 302 x 1 + 41

Step 3: We consider the new divisor 302 and the new remainder 41, and apply the division lemma to get

302 = 41 x 7 + 15

We consider the new divisor 41 and the new remainder 15,and apply the division lemma to get

41 = 15 x 2 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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 988 and 343 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(41,15) = HCF(302,41) = HCF(343,302) = HCF(988,343) .

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

Step 1: Since 224 > 1, we apply the division lemma to 224 and 1, to get

224 = 1 x 224 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 224 is 1

Notice that 1 = HCF(224,1) .

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Frequently Asked Questions on HCF of 988, 343, 224 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 988, 343, 224?

Answer: HCF of 988, 343, 224 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 988, 343, 224 using Euclid's Algorithm?

Answer: For arbitrary numbers 988, 343, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.