Highest Common Factor of 3504, 5460, 18521 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 3504, 5460, 18521 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3504, 5460, 18521 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 3504, 5460, 18521 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 3504, 5460, 18521 is 1.

HCF(3504, 5460, 18521) = 1

HCF of 3504, 5460, 18521 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 3504, 5460, 18521 is 1.

Highest Common Factor of 3504,5460,18521 using Euclid's algorithm

Highest Common Factor of 3504,5460,18521 is 1

Step 1: Since 5460 > 3504, we apply the division lemma to 5460 and 3504, to get

5460 = 3504 x 1 + 1956

Step 2: Since the reminder 3504 ≠ 0, we apply division lemma to 1956 and 3504, to get

3504 = 1956 x 1 + 1548

Step 3: We consider the new divisor 1956 and the new remainder 1548, and apply the division lemma to get

1956 = 1548 x 1 + 408

We consider the new divisor 1548 and the new remainder 408,and apply the division lemma to get

1548 = 408 x 3 + 324

We consider the new divisor 408 and the new remainder 324,and apply the division lemma to get

408 = 324 x 1 + 84

We consider the new divisor 324 and the new remainder 84,and apply the division lemma to get

324 = 84 x 3 + 72

We consider the new divisor 84 and the new remainder 72,and apply the division lemma to get

84 = 72 x 1 + 12

We consider the new divisor 72 and the new remainder 12,and apply the division lemma to get

72 = 12 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 3504 and 5460 is 12

Notice that 12 = HCF(72,12) = HCF(84,72) = HCF(324,84) = HCF(408,324) = HCF(1548,408) = HCF(1956,1548) = HCF(3504,1956) = HCF(5460,3504) .

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

Step 1: Since 18521 > 12, we apply the division lemma to 18521 and 12, to get

18521 = 12 x 1543 + 5

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 5 and 12, to get

12 = 5 x 2 + 2

Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get

5 = 2 x 2 + 1

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 12 and 18521 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(18521,12) .

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Frequently Asked Questions on HCF of 3504, 5460, 18521 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 3504, 5460, 18521?

Answer: HCF of 3504, 5460, 18521 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3504, 5460, 18521 using Euclid's Algorithm?

Answer: For arbitrary numbers 3504, 5460, 18521 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.