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 1016, 2086, 13376 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1016, 2086, 13376 is 2 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 1016, 2086, 13376 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 1016, 2086, 13376 is 2.
HCF(1016, 2086, 13376) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1016, 2086, 13376 is 2.
Step 1: Since 2086 > 1016, we apply the division lemma to 2086 and 1016, to get
2086 = 1016 x 2 + 54
Step 2: Since the reminder 1016 ≠ 0, we apply division lemma to 54 and 1016, to get
1016 = 54 x 18 + 44
Step 3: We consider the new divisor 54 and the new remainder 44, and apply the division lemma to get
54 = 44 x 1 + 10
We consider the new divisor 44 and the new remainder 10,and apply the division lemma to get
44 = 10 x 4 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1016 and 2086 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(44,10) = HCF(54,44) = HCF(1016,54) = HCF(2086,1016) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13376 > 2, we apply the division lemma to 13376 and 2, to get
13376 = 2 x 6688 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 13376 is 2
Notice that 2 = HCF(13376,2) .
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 1016, 2086, 13376?
Answer: HCF of 1016, 2086, 13376 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1016, 2086, 13376 using Euclid's Algorithm?
Answer: For arbitrary numbers 1016, 2086, 13376 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.