Highest Common Factor of 488, 178, 551 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 488, 178, 551 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 488, 178, 551 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 488, 178, 551 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 488, 178, 551 is 1.

HCF(488, 178, 551) = 1

HCF of 488, 178, 551 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 488, 178, 551 is 1.

Highest Common Factor of 488,178,551 using Euclid's algorithm

Highest Common Factor of 488,178,551 is 1

Step 1: Since 488 > 178, we apply the division lemma to 488 and 178, to get

488 = 178 x 2 + 132

Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 132 and 178, to get

178 = 132 x 1 + 46

Step 3: We consider the new divisor 132 and the new remainder 46, and apply the division lemma to get

132 = 46 x 2 + 40

We consider the new divisor 46 and the new remainder 40,and apply the division lemma to get

46 = 40 x 1 + 6

We consider the new divisor 40 and the new remainder 6,and apply the division lemma to get

40 = 6 x 6 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 488 and 178 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(46,40) = HCF(132,46) = HCF(178,132) = HCF(488,178) .

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

Step 1: Since 551 > 2, we apply the division lemma to 551 and 2, to get

551 = 2 x 275 + 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 551 is 1

Notice that 1 = HCF(2,1) = HCF(551,2) .

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Frequently Asked Questions on HCF of 488, 178, 551 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 488, 178, 551?

Answer: HCF of 488, 178, 551 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 488, 178, 551 using Euclid's Algorithm?

Answer: For arbitrary numbers 488, 178, 551 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.