Highest Common Factor of 446, 578, 324 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 446, 578, 324 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 446, 578, 324 is 2 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 446, 578, 324 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 446, 578, 324 is 2.

HCF(446, 578, 324) = 2

HCF of 446, 578, 324 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 446, 578, 324 is 2.

Highest Common Factor of 446,578,324 using Euclid's algorithm

Highest Common Factor of 446,578,324 is 2

Step 1: Since 578 > 446, we apply the division lemma to 578 and 446, to get

578 = 446 x 1 + 132

Step 2: Since the reminder 446 ≠ 0, we apply division lemma to 132 and 446, to get

446 = 132 x 3 + 50

Step 3: We consider the new divisor 132 and the new remainder 50, and apply the division lemma to get

132 = 50 x 2 + 32

We consider the new divisor 50 and the new remainder 32,and apply the division lemma to get

50 = 32 x 1 + 18

We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get

32 = 18 x 1 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 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 446 and 578 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(50,32) = HCF(132,50) = HCF(446,132) = HCF(578,446) .

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

Step 1: Since 324 > 2, we apply the division lemma to 324 and 2, to get

324 = 2 x 162 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 324 is 2

Notice that 2 = HCF(324,2) .

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Frequently Asked Questions on HCF of 446, 578, 324 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 446, 578, 324?

Answer: HCF of 446, 578, 324 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 446, 578, 324 using Euclid's Algorithm?

Answer: For arbitrary numbers 446, 578, 324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.