Highest Common Factor of 354, 667, 99 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 354, 667, 99 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 667, 99 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 354, 667, 99 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 354, 667, 99 is 1.

HCF(354, 667, 99) = 1

HCF of 354, 667, 99 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 354, 667, 99 is 1.

Highest Common Factor of 354,667,99 using Euclid's algorithm

Highest Common Factor of 354,667,99 is 1

Step 1: Since 667 > 354, we apply the division lemma to 667 and 354, to get

667 = 354 x 1 + 313

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 313 and 354, to get

354 = 313 x 1 + 41

Step 3: We consider the new divisor 313 and the new remainder 41, and apply the division lemma to get

313 = 41 x 7 + 26

We consider the new divisor 41 and the new remainder 26,and apply the division lemma to get

41 = 26 x 1 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 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 354 and 667 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(41,26) = HCF(313,41) = HCF(354,313) = HCF(667,354) .

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

Step 1: Since 99 > 1, we apply the division lemma to 99 and 1, to get

99 = 1 x 99 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 99 is 1

Notice that 1 = HCF(99,1) .

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Frequently Asked Questions on HCF of 354, 667, 99 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 354, 667, 99?

Answer: HCF of 354, 667, 99 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 667, 99 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 667, 99 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.