Highest Common Factor of 5480, 6546, 14688 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 5480, 6546, 14688 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 5480, 6546, 14688 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 5480, 6546, 14688 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 5480, 6546, 14688 is 2.

HCF(5480, 6546, 14688) = 2

HCF of 5480, 6546, 14688 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 5480, 6546, 14688 is 2.

Highest Common Factor of 5480,6546,14688 using Euclid's algorithm

Highest Common Factor of 5480,6546,14688 is 2

Step 1: Since 6546 > 5480, we apply the division lemma to 6546 and 5480, to get

6546 = 5480 x 1 + 1066

Step 2: Since the reminder 5480 ≠ 0, we apply division lemma to 1066 and 5480, to get

5480 = 1066 x 5 + 150

Step 3: We consider the new divisor 1066 and the new remainder 150, and apply the division lemma to get

1066 = 150 x 7 + 16

We consider the new divisor 150 and the new remainder 16,and apply the division lemma to get

150 = 16 x 9 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 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 5480 and 6546 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(150,16) = HCF(1066,150) = HCF(5480,1066) = HCF(6546,5480) .

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

Step 1: Since 14688 > 2, we apply the division lemma to 14688 and 2, to get

14688 = 2 x 7344 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 14688 is 2

Notice that 2 = HCF(14688,2) .

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Frequently Asked Questions on HCF of 5480, 6546, 14688 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 5480, 6546, 14688?

Answer: HCF of 5480, 6546, 14688 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5480, 6546, 14688 using Euclid's Algorithm?

Answer: For arbitrary numbers 5480, 6546, 14688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.