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 531, 1315, 9986 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 531, 1315, 9986 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 531, 1315, 9986 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 531, 1315, 9986 is 1.
HCF(531, 1315, 9986) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 531, 1315, 9986 is 1.
Step 1: Since 1315 > 531, we apply the division lemma to 1315 and 531, to get
1315 = 531 x 2 + 253
Step 2: Since the reminder 531 ≠ 0, we apply division lemma to 253 and 531, to get
531 = 253 x 2 + 25
Step 3: We consider the new divisor 253 and the new remainder 25, and apply the division lemma to get
253 = 25 x 10 + 3
We consider the new divisor 25 and the new remainder 3,and apply the division lemma to get
25 = 3 x 8 + 1
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 531 and 1315 is 1
Notice that 1 = HCF(3,1) = HCF(25,3) = HCF(253,25) = HCF(531,253) = HCF(1315,531) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9986 > 1, we apply the division lemma to 9986 and 1, to get
9986 = 1 x 9986 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9986 is 1
Notice that 1 = HCF(9986,1) .
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 531, 1315, 9986?
Answer: HCF of 531, 1315, 9986 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 531, 1315, 9986 using Euclid's Algorithm?
Answer: For arbitrary numbers 531, 1315, 9986 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.