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 6052, 5580, 41731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6052, 5580, 41731 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 6052, 5580, 41731 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 6052, 5580, 41731 is 1.
HCF(6052, 5580, 41731) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6052, 5580, 41731 is 1.
Step 1: Since 6052 > 5580, we apply the division lemma to 6052 and 5580, to get
6052 = 5580 x 1 + 472
Step 2: Since the reminder 5580 ≠ 0, we apply division lemma to 472 and 5580, to get
5580 = 472 x 11 + 388
Step 3: We consider the new divisor 472 and the new remainder 388, and apply the division lemma to get
472 = 388 x 1 + 84
We consider the new divisor 388 and the new remainder 84,and apply the division lemma to get
388 = 84 x 4 + 52
We consider the new divisor 84 and the new remainder 52,and apply the division lemma to get
84 = 52 x 1 + 32
We consider the new divisor 52 and the new remainder 32,and apply the division lemma to get
52 = 32 x 1 + 20
We consider the new divisor 32 and the new remainder 20,and apply the division lemma to get
32 = 20 x 1 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 6052 and 5580 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(52,32) = HCF(84,52) = HCF(388,84) = HCF(472,388) = HCF(5580,472) = HCF(6052,5580) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 41731 > 4, we apply the division lemma to 41731 and 4, to get
41731 = 4 x 10432 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 41731 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(41731,4) .
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 6052, 5580, 41731?
Answer: HCF of 6052, 5580, 41731 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6052, 5580, 41731 using Euclid's Algorithm?
Answer: For arbitrary numbers 6052, 5580, 41731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.