Highest Common Factor of 899, 344, 988 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 899, 344, 988 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 899, 344, 988 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 899, 344, 988 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 899, 344, 988 is 1.

HCF(899, 344, 988) = 1

HCF of 899, 344, 988 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 899, 344, 988 is 1.

Highest Common Factor of 899,344,988 using Euclid's algorithm

Highest Common Factor of 899,344,988 is 1

Step 1: Since 899 > 344, we apply the division lemma to 899 and 344, to get

899 = 344 x 2 + 211

Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 211 and 344, to get

344 = 211 x 1 + 133

Step 3: We consider the new divisor 211 and the new remainder 133, and apply the division lemma to get

211 = 133 x 1 + 78

We consider the new divisor 133 and the new remainder 78,and apply the division lemma to get

133 = 78 x 1 + 55

We consider the new divisor 78 and the new remainder 55,and apply the division lemma to get

78 = 55 x 1 + 23

We consider the new divisor 55 and the new remainder 23,and apply the division lemma to get

55 = 23 x 2 + 9

We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get

23 = 9 x 2 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 899 and 344 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(55,23) = HCF(78,55) = HCF(133,78) = HCF(211,133) = HCF(344,211) = HCF(899,344) .

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

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

988 = 1 x 988 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 988 is 1

Notice that 1 = HCF(988,1) .

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Frequently Asked Questions on HCF of 899, 344, 988 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 899, 344, 988?

Answer: HCF of 899, 344, 988 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 899, 344, 988 using Euclid's Algorithm?

Answer: For arbitrary numbers 899, 344, 988 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.