Highest Common Factor of 986, 908, 728 using Euclid's algorithm
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, 908, 728 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 986, 908, 728 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, 908, 728 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, 908, 728 is 2.
HCF(986, 908, 728) = 2
HCF of 986, 908, 728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 986, 908, 728 is 2.
Highest Common Factor of 986,908,728 is 2
Step 1: Since 986 > 908, we apply the division lemma to 986 and 908, to get
986 = 908 x 1 + 78
Step 2: Since the reminder 908 ≠ 0, we apply division lemma to 78 and 908, to get
908 = 78 x 11 + 50
Step 3: We consider the new divisor 78 and the new remainder 50, and apply the division lemma to get
78 = 50 x 1 + 28
We consider the new divisor 50 and the new remainder 28,and apply the division lemma to get
50 = 28 x 1 + 22
We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 986 and 908 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(50,28) = HCF(78,50) = HCF(908,78) = HCF(986,908) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 728 > 2, we apply the division lemma to 728 and 2, to get
728 = 2 x 364 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 728 is 2
Notice that 2 = HCF(728,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 986, 908, 728 using Euclid's Algorithm
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, 908, 728?
Answer: HCF of 986, 908, 728 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 986, 908, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 986, 908, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.