Highest Common Factor of 554, 919, 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 554, 919, 180 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 554, 919, 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 554, 919, 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 554, 919, 180 is 1.

HCF(554, 919, 180) = 1

HCF of 554, 919, 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 554, 919, 180 is 1.

Highest Common Factor of 554,919,180 using Euclid's algorithm

Highest Common Factor of 554,919,180 is 1

Step 1: Since 919 > 554, we apply the division lemma to 919 and 554, to get

919 = 554 x 1 + 365

Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 365 and 554, to get

554 = 365 x 1 + 189

Step 3: We consider the new divisor 365 and the new remainder 189, and apply the division lemma to get

365 = 189 x 1 + 176

We consider the new divisor 189 and the new remainder 176,and apply the division lemma to get

189 = 176 x 1 + 13

We consider the new divisor 176 and the new remainder 13,and apply the division lemma to get

176 = 13 x 13 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 554 and 919 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(176,13) = HCF(189,176) = HCF(365,189) = HCF(554,365) = HCF(919,554) .

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 554, 919, 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 554, 919, 180?

Answer: HCF of 554, 919, 180 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 554, 919, 180 using Euclid's Algorithm?

Answer: For arbitrary numbers 554, 919, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.