Highest Common Factor of 554, 292, 471 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, 292, 471 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 554, 292, 471 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, 292, 471 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, 292, 471 is 1.

HCF(554, 292, 471) = 1

HCF of 554, 292, 471 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, 292, 471 is 1.

Highest Common Factor of 554,292,471 using Euclid's algorithm

Highest Common Factor of 554,292,471 is 1

Step 1: Since 554 > 292, we apply the division lemma to 554 and 292, to get

554 = 292 x 1 + 262

Step 2: Since the reminder 292 ≠ 0, we apply division lemma to 262 and 292, to get

292 = 262 x 1 + 30

Step 3: We consider the new divisor 262 and the new remainder 30, and apply the division lemma to get

262 = 30 x 8 + 22

We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get

30 = 22 x 1 + 8

We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get

22 = 8 x 2 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 554 and 292 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(262,30) = HCF(292,262) = HCF(554,292) .

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

Step 1: Since 471 > 2, we apply the division lemma to 471 and 2, to get

471 = 2 x 235 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 471 is 1

Notice that 1 = HCF(2,1) = HCF(471,2) .

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Frequently Asked Questions on HCF of 554, 292, 471 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, 292, 471?

Answer: HCF of 554, 292, 471 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 554, 292, 471 using Euclid's Algorithm?

Answer: For arbitrary numbers 554, 292, 471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.