Highest Common Factor of 753, 297, 272 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 753, 297, 272 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 753, 297, 272 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 753, 297, 272 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 753, 297, 272 is 1.

HCF(753, 297, 272) = 1

HCF of 753, 297, 272 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 753, 297, 272 is 1.

Highest Common Factor of 753,297,272 using Euclid's algorithm

Highest Common Factor of 753,297,272 is 1

Step 1: Since 753 > 297, we apply the division lemma to 753 and 297, to get

753 = 297 x 2 + 159

Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 159 and 297, to get

297 = 159 x 1 + 138

Step 3: We consider the new divisor 159 and the new remainder 138, and apply the division lemma to get

159 = 138 x 1 + 21

We consider the new divisor 138 and the new remainder 21,and apply the division lemma to get

138 = 21 x 6 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 753 and 297 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(138,21) = HCF(159,138) = HCF(297,159) = HCF(753,297) .

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

Step 1: Since 272 > 3, we apply the division lemma to 272 and 3, to get

272 = 3 x 90 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 272 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(272,3) .

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Frequently Asked Questions on HCF of 753, 297, 272 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 753, 297, 272?

Answer: HCF of 753, 297, 272 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 753, 297, 272 using Euclid's Algorithm?

Answer: For arbitrary numbers 753, 297, 272 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.