Highest Common Factor of 7293, 2154, 53279 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 7293, 2154, 53279 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7293, 2154, 53279 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 7293, 2154, 53279 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 7293, 2154, 53279 is 1.

HCF(7293, 2154, 53279) = 1

HCF of 7293, 2154, 53279 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 7293, 2154, 53279 is 1.

Highest Common Factor of 7293,2154,53279 using Euclid's algorithm

Highest Common Factor of 7293,2154,53279 is 1

Step 1: Since 7293 > 2154, we apply the division lemma to 7293 and 2154, to get

7293 = 2154 x 3 + 831

Step 2: Since the reminder 2154 ≠ 0, we apply division lemma to 831 and 2154, to get

2154 = 831 x 2 + 492

Step 3: We consider the new divisor 831 and the new remainder 492, and apply the division lemma to get

831 = 492 x 1 + 339

We consider the new divisor 492 and the new remainder 339,and apply the division lemma to get

492 = 339 x 1 + 153

We consider the new divisor 339 and the new remainder 153,and apply the division lemma to get

339 = 153 x 2 + 33

We consider the new divisor 153 and the new remainder 33,and apply the division lemma to get

153 = 33 x 4 + 21

We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get

33 = 21 x 1 + 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 7293 and 2154 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(153,33) = HCF(339,153) = HCF(492,339) = HCF(831,492) = HCF(2154,831) = HCF(7293,2154) .

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

Step 1: Since 53279 > 3, we apply the division lemma to 53279 and 3, to get

53279 = 3 x 17759 + 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 53279 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(53279,3) .

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Frequently Asked Questions on HCF of 7293, 2154, 53279 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 7293, 2154, 53279?

Answer: HCF of 7293, 2154, 53279 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7293, 2154, 53279 using Euclid's Algorithm?

Answer: For arbitrary numbers 7293, 2154, 53279 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.