Highest Common Factor of 284, 390, 909 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 284, 390, 909 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 284, 390, 909 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 284, 390, 909 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 284, 390, 909 is 1.

HCF(284, 390, 909) = 1

HCF of 284, 390, 909 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 284, 390, 909 is 1.

Highest Common Factor of 284,390,909 using Euclid's algorithm

Highest Common Factor of 284,390,909 is 1

Step 1: Since 390 > 284, we apply the division lemma to 390 and 284, to get

390 = 284 x 1 + 106

Step 2: Since the reminder 284 ≠ 0, we apply division lemma to 106 and 284, to get

284 = 106 x 2 + 72

Step 3: We consider the new divisor 106 and the new remainder 72, and apply the division lemma to get

106 = 72 x 1 + 34

We consider the new divisor 72 and the new remainder 34,and apply the division lemma to get

72 = 34 x 2 + 4

We consider the new divisor 34 and the new remainder 4,and apply the division lemma to get

34 = 4 x 8 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 284 and 390 is 2

Notice that 2 = HCF(4,2) = HCF(34,4) = HCF(72,34) = HCF(106,72) = HCF(284,106) = HCF(390,284) .

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

Step 1: Since 909 > 2, we apply the division lemma to 909 and 2, to get

909 = 2 x 454 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 909 is 1

Notice that 1 = HCF(2,1) = HCF(909,2) .

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Frequently Asked Questions on HCF of 284, 390, 909 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 284, 390, 909?

Answer: HCF of 284, 390, 909 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 284, 390, 909 using Euclid's Algorithm?

Answer: For arbitrary numbers 284, 390, 909 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.