Highest Common Factor of 585, 944, 46 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, 944, 46 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 944, 46 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, 944, 46 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, 944, 46 is 1.

HCF(585, 944, 46) = 1

HCF of 585, 944, 46 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, 944, 46 is 1.

Highest Common Factor of 585,944,46 using Euclid's algorithm

Highest Common Factor of 585,944,46 is 1

Step 1: Since 944 > 585, we apply the division lemma to 944 and 585, to get

944 = 585 x 1 + 359

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 359 and 585, to get

585 = 359 x 1 + 226

Step 3: We consider the new divisor 359 and the new remainder 226, and apply the division lemma to get

359 = 226 x 1 + 133

We consider the new divisor 226 and the new remainder 133,and apply the division lemma to get

226 = 133 x 1 + 93

We consider the new divisor 133 and the new remainder 93,and apply the division lemma to get

133 = 93 x 1 + 40

We consider the new divisor 93 and the new remainder 40,and apply the division lemma to get

93 = 40 x 2 + 13

We consider the new divisor 40 and the new remainder 13,and apply the division lemma to get

40 = 13 x 3 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 585 and 944 is 1

Notice that 1 = HCF(13,1) = HCF(40,13) = HCF(93,40) = HCF(133,93) = HCF(226,133) = HCF(359,226) = HCF(585,359) = HCF(944,585) .

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

Step 1: Since 46 > 1, we apply the division lemma to 46 and 1, to get

46 = 1 x 46 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 46 is 1

Notice that 1 = HCF(46,1) .

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Frequently Asked Questions on HCF of 585, 944, 46 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, 944, 46?

Answer: HCF of 585, 944, 46 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 944, 46 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 944, 46 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.