Highest Common Factor of 654, 885, 90 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 654, 885, 90 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 654, 885, 90 is 3 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 654, 885, 90 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 654, 885, 90 is 3.

HCF(654, 885, 90) = 3

HCF of 654, 885, 90 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 654, 885, 90 is 3.

Highest Common Factor of 654,885,90 using Euclid's algorithm

Highest Common Factor of 654,885,90 is 3

Step 1: Since 885 > 654, we apply the division lemma to 885 and 654, to get

885 = 654 x 1 + 231

Step 2: Since the reminder 654 ≠ 0, we apply division lemma to 231 and 654, to get

654 = 231 x 2 + 192

Step 3: We consider the new divisor 231 and the new remainder 192, and apply the division lemma to get

231 = 192 x 1 + 39

We consider the new divisor 192 and the new remainder 39,and apply the division lemma to get

192 = 39 x 4 + 36

We consider the new divisor 39 and the new remainder 36,and apply the division lemma to get

39 = 36 x 1 + 3

We consider the new divisor 36 and the new remainder 3,and apply the division lemma to get

36 = 3 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 654 and 885 is 3

Notice that 3 = HCF(36,3) = HCF(39,36) = HCF(192,39) = HCF(231,192) = HCF(654,231) = HCF(885,654) .

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

Step 1: Since 90 > 3, we apply the division lemma to 90 and 3, to get

90 = 3 x 30 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 90 is 3

Notice that 3 = HCF(90,3) .

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Frequently Asked Questions on HCF of 654, 885, 90 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 654, 885, 90?

Answer: HCF of 654, 885, 90 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 654, 885, 90 using Euclid's Algorithm?

Answer: For arbitrary numbers 654, 885, 90 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.