Highest Common Factor of 285, 416, 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 285, 416, 46 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 285, 416, 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 285, 416, 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 285, 416, 46 is 1.

HCF(285, 416, 46) = 1

HCF of 285, 416, 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 285, 416, 46 is 1.

Highest Common Factor of 285,416,46 using Euclid's algorithm

Highest Common Factor of 285,416,46 is 1

Step 1: Since 416 > 285, we apply the division lemma to 416 and 285, to get

416 = 285 x 1 + 131

Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 131 and 285, to get

285 = 131 x 2 + 23

Step 3: We consider the new divisor 131 and the new remainder 23, and apply the division lemma to get

131 = 23 x 5 + 16

We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get

23 = 16 x 1 + 7

We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get

16 = 7 x 2 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 285 and 416 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(131,23) = HCF(285,131) = HCF(416,285) .

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 285, 416, 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 285, 416, 46?

Answer: HCF of 285, 416, 46 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 285, 416, 46 using Euclid's Algorithm?

Answer: For arbitrary numbers 285, 416, 46 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.