Highest Common Factor of 552, 1713 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 552, 1713 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 552, 1713 is 3 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 552, 1713 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 552, 1713 is 3.

HCF(552, 1713) = 3

HCF of 552, 1713 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 552, 1713 is 3.

Highest Common Factor of 552,1713 using Euclid's algorithm

Highest Common Factor of 552,1713 is 3

Step 1: Since 1713 > 552, we apply the division lemma to 1713 and 552, to get

1713 = 552 x 3 + 57

Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 57 and 552, to get

552 = 57 x 9 + 39

Step 3: We consider the new divisor 57 and the new remainder 39, and apply the division lemma to get

57 = 39 x 1 + 18

We consider the new divisor 39 and the new remainder 18,and apply the division lemma to get

39 = 18 x 2 + 3

We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get

18 = 3 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 552 and 1713 is 3

Notice that 3 = HCF(18,3) = HCF(39,18) = HCF(57,39) = HCF(552,57) = HCF(1713,552) .

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Frequently Asked Questions on HCF of 552, 1713 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 552, 1713?

Answer: HCF of 552, 1713 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 552, 1713 using Euclid's Algorithm?

Answer: For arbitrary numbers 552, 1713 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.