Highest Common Factor of 305, 816, 66 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 305, 816, 66 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 305, 816, 66 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 305, 816, 66 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 305, 816, 66 is 1.

HCF(305, 816, 66) = 1

HCF of 305, 816, 66 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 305, 816, 66 is 1.

Highest Common Factor of 305,816,66 using Euclid's algorithm

Highest Common Factor of 305,816,66 is 1

Step 1: Since 816 > 305, we apply the division lemma to 816 and 305, to get

816 = 305 x 2 + 206

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 206 and 305, to get

305 = 206 x 1 + 99

Step 3: We consider the new divisor 206 and the new remainder 99, and apply the division lemma to get

206 = 99 x 2 + 8

We consider the new divisor 99 and the new remainder 8,and apply the division lemma to get

99 = 8 x 12 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 305 and 816 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(99,8) = HCF(206,99) = HCF(305,206) = HCF(816,305) .

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

Step 1: Since 66 > 1, we apply the division lemma to 66 and 1, to get

66 = 1 x 66 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66 is 1

Notice that 1 = HCF(66,1) .

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Frequently Asked Questions on HCF of 305, 816, 66 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 305, 816, 66?

Answer: HCF of 305, 816, 66 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 305, 816, 66 using Euclid's Algorithm?

Answer: For arbitrary numbers 305, 816, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.