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 986, 8616, 1916 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 986, 8616, 1916 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 986, 8616, 1916 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 986, 8616, 1916 is 2.
HCF(986, 8616, 1916) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 986, 8616, 1916 is 2.
Step 1: Since 8616 > 986, we apply the division lemma to 8616 and 986, to get
8616 = 986 x 8 + 728
Step 2: Since the reminder 986 ≠ 0, we apply division lemma to 728 and 986, to get
986 = 728 x 1 + 258
Step 3: We consider the new divisor 728 and the new remainder 258, and apply the division lemma to get
728 = 258 x 2 + 212
We consider the new divisor 258 and the new remainder 212,and apply the division lemma to get
258 = 212 x 1 + 46
We consider the new divisor 212 and the new remainder 46,and apply the division lemma to get
212 = 46 x 4 + 28
We consider the new divisor 46 and the new remainder 28,and apply the division lemma to get
46 = 28 x 1 + 18
We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get
28 = 18 x 1 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 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 986 and 8616 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(46,28) = HCF(212,46) = HCF(258,212) = HCF(728,258) = HCF(986,728) = HCF(8616,986) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1916 > 2, we apply the division lemma to 1916 and 2, to get
1916 = 2 x 958 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 1916 is 2
Notice that 2 = HCF(1916,2) .
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 986, 8616, 1916?
Answer: HCF of 986, 8616, 1916 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 986, 8616, 1916 using Euclid's Algorithm?
Answer: For arbitrary numbers 986, 8616, 1916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.