Highest Common Factor of 5546, 7977, 32187 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 5546, 7977, 32187 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5546, 7977, 32187 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 5546, 7977, 32187 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 5546, 7977, 32187 is 1.

HCF(5546, 7977, 32187) = 1

HCF of 5546, 7977, 32187 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 5546, 7977, 32187 is 1.

Highest Common Factor of 5546,7977,32187 using Euclid's algorithm

Highest Common Factor of 5546,7977,32187 is 1

Step 1: Since 7977 > 5546, we apply the division lemma to 7977 and 5546, to get

7977 = 5546 x 1 + 2431

Step 2: Since the reminder 5546 ≠ 0, we apply division lemma to 2431 and 5546, to get

5546 = 2431 x 2 + 684

Step 3: We consider the new divisor 2431 and the new remainder 684, and apply the division lemma to get

2431 = 684 x 3 + 379

We consider the new divisor 684 and the new remainder 379,and apply the division lemma to get

684 = 379 x 1 + 305

We consider the new divisor 379 and the new remainder 305,and apply the division lemma to get

379 = 305 x 1 + 74

We consider the new divisor 305 and the new remainder 74,and apply the division lemma to get

305 = 74 x 4 + 9

We consider the new divisor 74 and the new remainder 9,and apply the division lemma to get

74 = 9 x 8 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 5546 and 7977 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(74,9) = HCF(305,74) = HCF(379,305) = HCF(684,379) = HCF(2431,684) = HCF(5546,2431) = HCF(7977,5546) .

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

Step 1: Since 32187 > 1, we apply the division lemma to 32187 and 1, to get

32187 = 1 x 32187 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32187 is 1

Notice that 1 = HCF(32187,1) .

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Frequently Asked Questions on HCF of 5546, 7977, 32187 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 5546, 7977, 32187?

Answer: HCF of 5546, 7977, 32187 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5546, 7977, 32187 using Euclid's Algorithm?

Answer: For arbitrary numbers 5546, 7977, 32187 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.