Highest Common Factor of 1753, 992 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 1753, 992 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1753, 992 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 1753, 992 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 1753, 992 is 1.

HCF(1753, 992) = 1

HCF of 1753, 992 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 1753, 992 is 1.

Highest Common Factor of 1753,992 using Euclid's algorithm

Highest Common Factor of 1753,992 is 1

Step 1: Since 1753 > 992, we apply the division lemma to 1753 and 992, to get

1753 = 992 x 1 + 761

Step 2: Since the reminder 992 ≠ 0, we apply division lemma to 761 and 992, to get

992 = 761 x 1 + 231

Step 3: We consider the new divisor 761 and the new remainder 231, and apply the division lemma to get

761 = 231 x 3 + 68

We consider the new divisor 231 and the new remainder 68,and apply the division lemma to get

231 = 68 x 3 + 27

We consider the new divisor 68 and the new remainder 27,and apply the division lemma to get

68 = 27 x 2 + 14

We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1753 and 992 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(68,27) = HCF(231,68) = HCF(761,231) = HCF(992,761) = HCF(1753,992) .

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Frequently Asked Questions on HCF of 1753, 992 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 1753, 992?

Answer: HCF of 1753, 992 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1753, 992 using Euclid's Algorithm?

Answer: For arbitrary numbers 1753, 992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.