Highest Common Factor of 888, 723, 146 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 888, 723, 146 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 888, 723, 146 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 888, 723, 146 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 888, 723, 146 is 1.

HCF(888, 723, 146) = 1

HCF of 888, 723, 146 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 888, 723, 146 is 1.

Highest Common Factor of 888,723,146 using Euclid's algorithm

Highest Common Factor of 888,723,146 is 1

Step 1: Since 888 > 723, we apply the division lemma to 888 and 723, to get

888 = 723 x 1 + 165

Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 165 and 723, to get

723 = 165 x 4 + 63

Step 3: We consider the new divisor 165 and the new remainder 63, and apply the division lemma to get

165 = 63 x 2 + 39

We consider the new divisor 63 and the new remainder 39,and apply the division lemma to get

63 = 39 x 1 + 24

We consider the new divisor 39 and the new remainder 24,and apply the division lemma to get

39 = 24 x 1 + 15

We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 888 and 723 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(63,39) = HCF(165,63) = HCF(723,165) = HCF(888,723) .

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

Step 1: Since 146 > 3, we apply the division lemma to 146 and 3, to get

146 = 3 x 48 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 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 3 and 146 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(146,3) .

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Frequently Asked Questions on HCF of 888, 723, 146 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 888, 723, 146?

Answer: HCF of 888, 723, 146 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 888, 723, 146 using Euclid's Algorithm?

Answer: For arbitrary numbers 888, 723, 146 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.