Highest Common Factor of 999, 688, 318 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 999, 688, 318 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 999, 688, 318 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 999, 688, 318 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 999, 688, 318 is 1.

HCF(999, 688, 318) = 1

HCF of 999, 688, 318 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 999, 688, 318 is 1.

Highest Common Factor of 999,688,318 using Euclid's algorithm

Highest Common Factor of 999,688,318 is 1

Step 1: Since 999 > 688, we apply the division lemma to 999 and 688, to get

999 = 688 x 1 + 311

Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 311 and 688, to get

688 = 311 x 2 + 66

Step 3: We consider the new divisor 311 and the new remainder 66, and apply the division lemma to get

311 = 66 x 4 + 47

We consider the new divisor 66 and the new remainder 47,and apply the division lemma to get

66 = 47 x 1 + 19

We consider the new divisor 47 and the new remainder 19,and apply the division lemma to get

47 = 19 x 2 + 9

We consider the new divisor 19 and the new remainder 9,and apply the division lemma to get

19 = 9 x 2 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 999 and 688 is 1

Notice that 1 = HCF(9,1) = HCF(19,9) = HCF(47,19) = HCF(66,47) = HCF(311,66) = HCF(688,311) = HCF(999,688) .

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

Step 1: Since 318 > 1, we apply the division lemma to 318 and 1, to get

318 = 1 x 318 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 318 is 1

Notice that 1 = HCF(318,1) .

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Frequently Asked Questions on HCF of 999, 688, 318 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 999, 688, 318?

Answer: HCF of 999, 688, 318 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 999, 688, 318 using Euclid's Algorithm?

Answer: For arbitrary numbers 999, 688, 318 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.