Highest Common Factor of 986, 38310 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, 38310 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 986, 38310 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, 38310 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, 38310 is 2.
HCF(986, 38310) = 2
HCF of 986, 38310 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, 38310 is 2.
Highest Common Factor of 986,38310 is 2
Step 1: Since 38310 > 986, we apply the division lemma to 38310 and 986, to get
38310 = 986 x 38 + 842
Step 2: Since the reminder 986 ≠ 0, we apply division lemma to 842 and 986, to get
986 = 842 x 1 + 144
Step 3: We consider the new divisor 842 and the new remainder 144, and apply the division lemma to get
842 = 144 x 5 + 122
We consider the new divisor 144 and the new remainder 122,and apply the division lemma to get
144 = 122 x 1 + 22
We consider the new divisor 122 and the new remainder 22,and apply the division lemma to get
122 = 22 x 5 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 986 and 38310 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(122,22) = HCF(144,122) = HCF(842,144) = HCF(986,842) = HCF(38310,986) .
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, 38310 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, 38310?
Answer: HCF of 986, 38310 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 986, 38310 using Euclid's Algorithm?
Answer: For arbitrary numbers 986, 38310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
