Highest Common Factor of 285, 760, 882 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, 760, 882 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 285, 760, 882 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, 760, 882 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, 760, 882 is 1.

HCF(285, 760, 882) = 1

HCF of 285, 760, 882 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, 760, 882 is 1.

Highest Common Factor of 285,760,882 using Euclid's algorithm

Highest Common Factor of 285,760,882 is 1

Step 1: Since 760 > 285, we apply the division lemma to 760 and 285, to get

760 = 285 x 2 + 190

Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 190 and 285, to get

285 = 190 x 1 + 95

Step 3: We consider the new divisor 190 and the new remainder 95, and apply the division lemma to get

190 = 95 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 95, the HCF of 285 and 760 is 95

Notice that 95 = HCF(190,95) = HCF(285,190) = HCF(760,285) .

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

Step 1: Since 882 > 95, we apply the division lemma to 882 and 95, to get

882 = 95 x 9 + 27

Step 2: Since the reminder 95 ≠ 0, we apply division lemma to 27 and 95, to get

95 = 27 x 3 + 14

Step 3: We consider the new divisor 27 and the new remainder 14, and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 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 95 and 882 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(95,27) = HCF(882,95) .

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Frequently Asked Questions on HCF of 285, 760, 882 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, 760, 882?

Answer: HCF of 285, 760, 882 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 285, 760, 882 using Euclid's Algorithm?

Answer: For arbitrary numbers 285, 760, 882 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.