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 6616, 8916, 24524 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 6616, 8916, 24524 is 4 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 6616, 8916, 24524 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 6616, 8916, 24524 is 4.
HCF(6616, 8916, 24524) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6616, 8916, 24524 is 4.
Step 1: Since 8916 > 6616, we apply the division lemma to 8916 and 6616, to get
8916 = 6616 x 1 + 2300
Step 2: Since the reminder 6616 ≠ 0, we apply division lemma to 2300 and 6616, to get
6616 = 2300 x 2 + 2016
Step 3: We consider the new divisor 2300 and the new remainder 2016, and apply the division lemma to get
2300 = 2016 x 1 + 284
We consider the new divisor 2016 and the new remainder 284,and apply the division lemma to get
2016 = 284 x 7 + 28
We consider the new divisor 284 and the new remainder 28,and apply the division lemma to get
284 = 28 x 10 + 4
We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get
28 = 4 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 6616 and 8916 is 4
Notice that 4 = HCF(28,4) = HCF(284,28) = HCF(2016,284) = HCF(2300,2016) = HCF(6616,2300) = HCF(8916,6616) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 24524 > 4, we apply the division lemma to 24524 and 4, to get
24524 = 4 x 6131 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 24524 is 4
Notice that 4 = HCF(24524,4) .
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 6616, 8916, 24524?
Answer: HCF of 6616, 8916, 24524 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6616, 8916, 24524 using Euclid's Algorithm?
Answer: For arbitrary numbers 6616, 8916, 24524 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.