Highest Common Factor of 678, 399, 188 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 678, 399, 188 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 678, 399, 188 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 678, 399, 188 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 678, 399, 188 is 1.

HCF(678, 399, 188) = 1

HCF of 678, 399, 188 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 678, 399, 188 is 1.

Highest Common Factor of 678,399,188 using Euclid's algorithm

Highest Common Factor of 678,399,188 is 1

Step 1: Since 678 > 399, we apply the division lemma to 678 and 399, to get

678 = 399 x 1 + 279

Step 2: Since the reminder 399 ≠ 0, we apply division lemma to 279 and 399, to get

399 = 279 x 1 + 120

Step 3: We consider the new divisor 279 and the new remainder 120, and apply the division lemma to get

279 = 120 x 2 + 39

We consider the new divisor 120 and the new remainder 39,and apply the division lemma to get

120 = 39 x 3 + 3

We consider the new divisor 39 and the new remainder 3,and apply the division lemma to get

39 = 3 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 678 and 399 is 3

Notice that 3 = HCF(39,3) = HCF(120,39) = HCF(279,120) = HCF(399,279) = HCF(678,399) .

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

Step 1: Since 188 > 3, we apply the division lemma to 188 and 3, to get

188 = 3 x 62 + 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 188 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(188,3) .

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Frequently Asked Questions on HCF of 678, 399, 188 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 678, 399, 188?

Answer: HCF of 678, 399, 188 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 678, 399, 188 using Euclid's Algorithm?

Answer: For arbitrary numbers 678, 399, 188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.