Highest Common Factor of 365, 496, 554 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 365, 496, 554 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 365, 496, 554 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 365, 496, 554 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 365, 496, 554 is 1.

HCF(365, 496, 554) = 1

HCF of 365, 496, 554 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 365, 496, 554 is 1.

Highest Common Factor of 365,496,554 using Euclid's algorithm

Highest Common Factor of 365,496,554 is 1

Step 1: Since 496 > 365, we apply the division lemma to 496 and 365, to get

496 = 365 x 1 + 131

Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 131 and 365, to get

365 = 131 x 2 + 103

Step 3: We consider the new divisor 131 and the new remainder 103, and apply the division lemma to get

131 = 103 x 1 + 28

We consider the new divisor 103 and the new remainder 28,and apply the division lemma to get

103 = 28 x 3 + 19

We consider the new divisor 28 and the new remainder 19,and apply the division lemma to get

28 = 19 x 1 + 9

We consider the new divisor 19 and the new remainder 9,and apply the division lemma to get

19 = 9 x 2 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 365 and 496 is 1

Notice that 1 = HCF(9,1) = HCF(19,9) = HCF(28,19) = HCF(103,28) = HCF(131,103) = HCF(365,131) = HCF(496,365) .

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

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

554 = 1 x 554 + 0

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

Notice that 1 = HCF(554,1) .

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Frequently Asked Questions on HCF of 365, 496, 554 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 365, 496, 554?

Answer: HCF of 365, 496, 554 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 365, 496, 554 using Euclid's Algorithm?

Answer: For arbitrary numbers 365, 496, 554 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.