Highest Common Factor of 585, 740, 427 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 585, 740, 427 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 740, 427 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 585, 740, 427 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 585, 740, 427 is 1.

HCF(585, 740, 427) = 1

HCF of 585, 740, 427 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 585, 740, 427 is 1.

Highest Common Factor of 585,740,427 using Euclid's algorithm

Highest Common Factor of 585,740,427 is 1

Step 1: Since 740 > 585, we apply the division lemma to 740 and 585, to get

740 = 585 x 1 + 155

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 155 and 585, to get

585 = 155 x 3 + 120

Step 3: We consider the new divisor 155 and the new remainder 120, and apply the division lemma to get

155 = 120 x 1 + 35

We consider the new divisor 120 and the new remainder 35,and apply the division lemma to get

120 = 35 x 3 + 15

We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get

35 = 15 x 2 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 585 and 740 is 5

Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(120,35) = HCF(155,120) = HCF(585,155) = HCF(740,585) .

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

Step 1: Since 427 > 5, we apply the division lemma to 427 and 5, to get

427 = 5 x 85 + 2

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

5 = 2 x 2 + 1

Step 3: 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 5 and 427 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(427,5) .

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Frequently Asked Questions on HCF of 585, 740, 427 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 585, 740, 427?

Answer: HCF of 585, 740, 427 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 740, 427 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 740, 427 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.