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 6540, 1884 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 6540, 1884 is 12 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 6540, 1884 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 6540, 1884 is 12.
HCF(6540, 1884) = 12
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6540, 1884 is 12.
Step 1: Since 6540 > 1884, we apply the division lemma to 6540 and 1884, to get
6540 = 1884 x 3 + 888
Step 2: Since the reminder 1884 ≠ 0, we apply division lemma to 888 and 1884, to get
1884 = 888 x 2 + 108
Step 3: We consider the new divisor 888 and the new remainder 108, and apply the division lemma to get
888 = 108 x 8 + 24
We consider the new divisor 108 and the new remainder 24,and apply the division lemma to get
108 = 24 x 4 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 6540 and 1884 is 12
Notice that 12 = HCF(24,12) = HCF(108,24) = HCF(888,108) = HCF(1884,888) = HCF(6540,1884) .
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 6540, 1884?
Answer: HCF of 6540, 1884 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6540, 1884 using Euclid's Algorithm?
Answer: For arbitrary numbers 6540, 1884 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.