Highest Common Factor of 738, 460, 300 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 738, 460, 300 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 738, 460, 300 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 738, 460, 300 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 738, 460, 300 is 2.

HCF(738, 460, 300) = 2

HCF of 738, 460, 300 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 738, 460, 300 is 2.

Highest Common Factor of 738,460,300 using Euclid's algorithm

Highest Common Factor of 738,460,300 is 2

Step 1: Since 738 > 460, we apply the division lemma to 738 and 460, to get

738 = 460 x 1 + 278

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 278 and 460, to get

460 = 278 x 1 + 182

Step 3: We consider the new divisor 278 and the new remainder 182, and apply the division lemma to get

278 = 182 x 1 + 96

We consider the new divisor 182 and the new remainder 96,and apply the division lemma to get

182 = 96 x 1 + 86

We consider the new divisor 96 and the new remainder 86,and apply the division lemma to get

96 = 86 x 1 + 10

We consider the new divisor 86 and the new remainder 10,and apply the division lemma to get

86 = 10 x 8 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 738 and 460 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(86,10) = HCF(96,86) = HCF(182,96) = HCF(278,182) = HCF(460,278) = HCF(738,460) .

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

Step 1: Since 300 > 2, we apply the division lemma to 300 and 2, to get

300 = 2 x 150 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 300 is 2

Notice that 2 = HCF(300,2) .

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Frequently Asked Questions on HCF of 738, 460, 300 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 738, 460, 300?

Answer: HCF of 738, 460, 300 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 738, 460, 300 using Euclid's Algorithm?

Answer: For arbitrary numbers 738, 460, 300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.