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 1731, 9792 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1731, 9792 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 1731, 9792 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 1731, 9792 is 3.
HCF(1731, 9792) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1731, 9792 is 3.
Step 1: Since 9792 > 1731, we apply the division lemma to 9792 and 1731, to get
9792 = 1731 x 5 + 1137
Step 2: Since the reminder 1731 ≠ 0, we apply division lemma to 1137 and 1731, to get
1731 = 1137 x 1 + 594
Step 3: We consider the new divisor 1137 and the new remainder 594, and apply the division lemma to get
1137 = 594 x 1 + 543
We consider the new divisor 594 and the new remainder 543,and apply the division lemma to get
594 = 543 x 1 + 51
We consider the new divisor 543 and the new remainder 51,and apply the division lemma to get
543 = 51 x 10 + 33
We consider the new divisor 51 and the new remainder 33,and apply the division lemma to get
51 = 33 x 1 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1731 and 9792 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) = HCF(543,51) = HCF(594,543) = HCF(1137,594) = HCF(1731,1137) = HCF(9792,1731) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 1731, 9792?
Answer: HCF of 1731, 9792 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1731, 9792 using Euclid's Algorithm?
Answer: For arbitrary numbers 1731, 9792 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.