Highest Common Factor of 380, 699, 180 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 380, 699, 180 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 380, 699, 180 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 380, 699, 180 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 380, 699, 180 is 1.

HCF(380, 699, 180) = 1

HCF of 380, 699, 180 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 380, 699, 180 is 1.

Highest Common Factor of 380,699,180 using Euclid's algorithm

Highest Common Factor of 380,699,180 is 1

Step 1: Since 699 > 380, we apply the division lemma to 699 and 380, to get

699 = 380 x 1 + 319

Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 319 and 380, to get

380 = 319 x 1 + 61

Step 3: We consider the new divisor 319 and the new remainder 61, and apply the division lemma to get

319 = 61 x 5 + 14

We consider the new divisor 61 and the new remainder 14,and apply the division lemma to get

61 = 14 x 4 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 380 and 699 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(61,14) = HCF(319,61) = HCF(380,319) = HCF(699,380) .

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

Step 1: Since 180 > 1, we apply the division lemma to 180 and 1, to get

180 = 1 x 180 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 180 is 1

Notice that 1 = HCF(180,1) .

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Frequently Asked Questions on HCF of 380, 699, 180 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 380, 699, 180?

Answer: HCF of 380, 699, 180 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 380, 699, 180 using Euclid's Algorithm?

Answer: For arbitrary numbers 380, 699, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.