Highest Common Factor of 888, 660, 119 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, 660, 119 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 888, 660, 119 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, 660, 119 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, 660, 119 is 1.

HCF(888, 660, 119) = 1

HCF of 888, 660, 119 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, 660, 119 is 1.

Highest Common Factor of 888,660,119 using Euclid's algorithm

Highest Common Factor of 888,660,119 is 1

Step 1: Since 888 > 660, we apply the division lemma to 888 and 660, to get

888 = 660 x 1 + 228

Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 228 and 660, to get

660 = 228 x 2 + 204

Step 3: We consider the new divisor 228 and the new remainder 204, and apply the division lemma to get

228 = 204 x 1 + 24

We consider the new divisor 204 and the new remainder 24,and apply the division lemma to get

204 = 24 x 8 + 12

We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get

24 = 12 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 888 and 660 is 12

Notice that 12 = HCF(24,12) = HCF(204,24) = HCF(228,204) = HCF(660,228) = HCF(888,660) .


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

Step 1: Since 119 > 12, we apply the division lemma to 119 and 12, to get

119 = 12 x 9 + 11

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 11 and 12, to get

12 = 11 x 1 + 1

Step 3: We consider the new divisor 11 and the new remainder 1, and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 119 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(119,12) .

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Frequently Asked Questions on HCF of 888, 660, 119 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, 660, 119?

Answer: HCF of 888, 660, 119 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 888, 660, 119 using Euclid's Algorithm?

Answer: For arbitrary numbers 888, 660, 119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.