Highest Common Factor of 990, 155, 306 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 990, 155, 306 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 990, 155, 306 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 990, 155, 306 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 990, 155, 306 is 1.

HCF(990, 155, 306) = 1

HCF of 990, 155, 306 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 990, 155, 306 is 1.

Highest Common Factor of 990,155,306 using Euclid's algorithm

Highest Common Factor of 990,155,306 is 1

Step 1: Since 990 > 155, we apply the division lemma to 990 and 155, to get

990 = 155 x 6 + 60

Step 2: Since the reminder 155 ≠ 0, we apply division lemma to 60 and 155, to get

155 = 60 x 2 + 35

Step 3: We consider the new divisor 60 and the new remainder 35, and apply the division lemma to get

60 = 35 x 1 + 25

We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get

35 = 25 x 1 + 10

We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get

25 = 10 x 2 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 990 and 155 is 5

Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(60,35) = HCF(155,60) = HCF(990,155) .

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

Step 1: Since 306 > 5, we apply the division lemma to 306 and 5, to get

306 = 5 x 61 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 306 is 1

Notice that 1 = HCF(5,1) = HCF(306,5) .

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Frequently Asked Questions on HCF of 990, 155, 306 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 990, 155, 306?

Answer: HCF of 990, 155, 306 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 990, 155, 306 using Euclid's Algorithm?

Answer: For arbitrary numbers 990, 155, 306 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.