Highest Common Factor of 2722, 4977, 17224 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 2722, 4977, 17224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2722, 4977, 17224 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 2722, 4977, 17224 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 2722, 4977, 17224 is 1.

HCF(2722, 4977, 17224) = 1

HCF of 2722, 4977, 17224 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 2722, 4977, 17224 is 1.

Highest Common Factor of 2722,4977,17224 using Euclid's algorithm

Highest Common Factor of 2722,4977,17224 is 1

Step 1: Since 4977 > 2722, we apply the division lemma to 4977 and 2722, to get

4977 = 2722 x 1 + 2255

Step 2: Since the reminder 2722 ≠ 0, we apply division lemma to 2255 and 2722, to get

2722 = 2255 x 1 + 467

Step 3: We consider the new divisor 2255 and the new remainder 467, and apply the division lemma to get

2255 = 467 x 4 + 387

We consider the new divisor 467 and the new remainder 387,and apply the division lemma to get

467 = 387 x 1 + 80

We consider the new divisor 387 and the new remainder 80,and apply the division lemma to get

387 = 80 x 4 + 67

We consider the new divisor 80 and the new remainder 67,and apply the division lemma to get

80 = 67 x 1 + 13

We consider the new divisor 67 and the new remainder 13,and apply the division lemma to get

67 = 13 x 5 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 2722 and 4977 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(67,13) = HCF(80,67) = HCF(387,80) = HCF(467,387) = HCF(2255,467) = HCF(2722,2255) = HCF(4977,2722) .

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

Step 1: Since 17224 > 1, we apply the division lemma to 17224 and 1, to get

17224 = 1 x 17224 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 17224 is 1

Notice that 1 = HCF(17224,1) .

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Frequently Asked Questions on HCF of 2722, 4977, 17224 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 2722, 4977, 17224?

Answer: HCF of 2722, 4977, 17224 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2722, 4977, 17224 using Euclid's Algorithm?

Answer: For arbitrary numbers 2722, 4977, 17224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.