Highest Common Factor of 594, 374, 496 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 594, 374, 496 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 594, 374, 496 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 594, 374, 496 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 594, 374, 496 is 2.

HCF(594, 374, 496) = 2

HCF of 594, 374, 496 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 594, 374, 496 is 2.

Highest Common Factor of 594,374,496 using Euclid's algorithm

Highest Common Factor of 594,374,496 is 2

Step 1: Since 594 > 374, we apply the division lemma to 594 and 374, to get

594 = 374 x 1 + 220

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 220 and 374, to get

374 = 220 x 1 + 154

Step 3: We consider the new divisor 220 and the new remainder 154, and apply the division lemma to get

220 = 154 x 1 + 66

We consider the new divisor 154 and the new remainder 66,and apply the division lemma to get

154 = 66 x 2 + 22

We consider the new divisor 66 and the new remainder 22,and apply the division lemma to get

66 = 22 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 594 and 374 is 22

Notice that 22 = HCF(66,22) = HCF(154,66) = HCF(220,154) = HCF(374,220) = HCF(594,374) .

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

Step 1: Since 496 > 22, we apply the division lemma to 496 and 22, to get

496 = 22 x 22 + 12

Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 12 and 22, to get

22 = 12 x 1 + 10

Step 3: We consider the new divisor 12 and the new remainder 10, and apply the division lemma to get

12 = 10 x 1 + 2

We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 22 and 496 is 2

Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(496,22) .

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Frequently Asked Questions on HCF of 594, 374, 496 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 594, 374, 496?

Answer: HCF of 594, 374, 496 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 594, 374, 496 using Euclid's Algorithm?

Answer: For arbitrary numbers 594, 374, 496 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.