Highest Common Factor of 420, 753, 548 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 420, 753, 548 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 753, 548 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 420, 753, 548 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 420, 753, 548 is 1.

HCF(420, 753, 548) = 1

HCF of 420, 753, 548 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 420, 753, 548 is 1.

Highest Common Factor of 420,753,548 using Euclid's algorithm

Highest Common Factor of 420,753,548 is 1

Step 1: Since 753 > 420, we apply the division lemma to 753 and 420, to get

753 = 420 x 1 + 333

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 333 and 420, to get

420 = 333 x 1 + 87

Step 3: We consider the new divisor 333 and the new remainder 87, and apply the division lemma to get

333 = 87 x 3 + 72

We consider the new divisor 87 and the new remainder 72,and apply the division lemma to get

87 = 72 x 1 + 15

We consider the new divisor 72 and the new remainder 15,and apply the division lemma to get

72 = 15 x 4 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 420 and 753 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(72,15) = HCF(87,72) = HCF(333,87) = HCF(420,333) = HCF(753,420) .

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

Step 1: Since 548 > 3, we apply the division lemma to 548 and 3, to get

548 = 3 x 182 + 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 548 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(548,3) .

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Frequently Asked Questions on HCF of 420, 753, 548 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 420, 753, 548?

Answer: HCF of 420, 753, 548 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 753, 548 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 753, 548 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.