Highest Common Factor of 5574, 8908, 54525 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 5574, 8908, 54525 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5574, 8908, 54525 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 5574, 8908, 54525 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 5574, 8908, 54525 is 1.

HCF(5574, 8908, 54525) = 1

HCF of 5574, 8908, 54525 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 5574, 8908, 54525 is 1.

Highest Common Factor of 5574,8908,54525 using Euclid's algorithm

Highest Common Factor of 5574,8908,54525 is 1

Step 1: Since 8908 > 5574, we apply the division lemma to 8908 and 5574, to get

8908 = 5574 x 1 + 3334

Step 2: Since the reminder 5574 ≠ 0, we apply division lemma to 3334 and 5574, to get

5574 = 3334 x 1 + 2240

Step 3: We consider the new divisor 3334 and the new remainder 2240, and apply the division lemma to get

3334 = 2240 x 1 + 1094

We consider the new divisor 2240 and the new remainder 1094,and apply the division lemma to get

2240 = 1094 x 2 + 52

We consider the new divisor 1094 and the new remainder 52,and apply the division lemma to get

1094 = 52 x 21 + 2

We consider the new divisor 52 and the new remainder 2,and apply the division lemma to get

52 = 2 x 26 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5574 and 8908 is 2

Notice that 2 = HCF(52,2) = HCF(1094,52) = HCF(2240,1094) = HCF(3334,2240) = HCF(5574,3334) = HCF(8908,5574) .

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

Step 1: Since 54525 > 2, we apply the division lemma to 54525 and 2, to get

54525 = 2 x 27262 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 54525 is 1

Notice that 1 = HCF(2,1) = HCF(54525,2) .

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Frequently Asked Questions on HCF of 5574, 8908, 54525 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 5574, 8908, 54525?

Answer: HCF of 5574, 8908, 54525 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5574, 8908, 54525 using Euclid's Algorithm?

Answer: For arbitrary numbers 5574, 8908, 54525 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.