Highest Common Factor of 374, 512, 738 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 374, 512, 738 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 374, 512, 738 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 374, 512, 738 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 374, 512, 738 is 2.

HCF(374, 512, 738) = 2

HCF of 374, 512, 738 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 374, 512, 738 is 2.

Highest Common Factor of 374,512,738 using Euclid's algorithm

Highest Common Factor of 374,512,738 is 2

Step 1: Since 512 > 374, we apply the division lemma to 512 and 374, to get

512 = 374 x 1 + 138

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 138 and 374, to get

374 = 138 x 2 + 98

Step 3: We consider the new divisor 138 and the new remainder 98, and apply the division lemma to get

138 = 98 x 1 + 40

We consider the new divisor 98 and the new remainder 40,and apply the division lemma to get

98 = 40 x 2 + 18

We consider the new divisor 40 and the new remainder 18,and apply the division lemma to get

40 = 18 x 2 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 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 374 and 512 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(40,18) = HCF(98,40) = HCF(138,98) = HCF(374,138) = HCF(512,374) .

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

Step 1: Since 738 > 2, we apply the division lemma to 738 and 2, to get

738 = 2 x 369 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 738 is 2

Notice that 2 = HCF(738,2) .

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Frequently Asked Questions on HCF of 374, 512, 738 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 374, 512, 738?

Answer: HCF of 374, 512, 738 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 374, 512, 738 using Euclid's Algorithm?

Answer: For arbitrary numbers 374, 512, 738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.