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 886, 516, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 886, 516, 21 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 886, 516, 21 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 886, 516, 21 is 1.
HCF(886, 516, 21) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 886, 516, 21 is 1.
Step 1: Since 886 > 516, we apply the division lemma to 886 and 516, to get
886 = 516 x 1 + 370
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 370 and 516, to get
516 = 370 x 1 + 146
Step 3: We consider the new divisor 370 and the new remainder 146, and apply the division lemma to get
370 = 146 x 2 + 78
We consider the new divisor 146 and the new remainder 78,and apply the division lemma to get
146 = 78 x 1 + 68
We consider the new divisor 78 and the new remainder 68,and apply the division lemma to get
78 = 68 x 1 + 10
We consider the new divisor 68 and the new remainder 10,and apply the division lemma to get
68 = 10 x 6 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 886 and 516 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(68,10) = HCF(78,68) = HCF(146,78) = HCF(370,146) = HCF(516,370) = HCF(886,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 2, we apply the division lemma to 21 and 2, to get
21 = 2 x 10 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 21 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) .
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 886, 516, 21?
Answer: HCF of 886, 516, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 886, 516, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 886, 516, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.