Highest Common Factor of 2730, 2004 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 2730, 2004 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 2730, 2004 is 6 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 2730, 2004 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 2730, 2004 is 6.
HCF(2730, 2004) = 6
HCF of 2730, 2004 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2730, 2004 is 6.
Highest Common Factor of 2730,2004 is 6
Step 1: Since 2730 > 2004, we apply the division lemma to 2730 and 2004, to get
2730 = 2004 x 1 + 726
Step 2: Since the reminder 2004 ≠ 0, we apply division lemma to 726 and 2004, to get
2004 = 726 x 2 + 552
Step 3: We consider the new divisor 726 and the new remainder 552, and apply the division lemma to get
726 = 552 x 1 + 174
We consider the new divisor 552 and the new remainder 174,and apply the division lemma to get
552 = 174 x 3 + 30
We consider the new divisor 174 and the new remainder 30,and apply the division lemma to get
174 = 30 x 5 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 2730 and 2004 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(174,30) = HCF(552,174) = HCF(726,552) = HCF(2004,726) = HCF(2730,2004) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2730, 2004 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 2730, 2004?
Answer: HCF of 2730, 2004 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2730, 2004 using Euclid's Algorithm?
Answer: For arbitrary numbers 2730, 2004 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.