Highest Common Factor of 982, 8585 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 982, 8585 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 982, 8585 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 982, 8585 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 982, 8585 is 1.
HCF(982, 8585) = 1
HCF of 982, 8585 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 982, 8585 is 1.
Highest Common Factor of 982,8585 is 1
Step 1: Since 8585 > 982, we apply the division lemma to 8585 and 982, to get
8585 = 982 x 8 + 729
Step 2: Since the reminder 982 ≠ 0, we apply division lemma to 729 and 982, to get
982 = 729 x 1 + 253
Step 3: We consider the new divisor 729 and the new remainder 253, and apply the division lemma to get
729 = 253 x 2 + 223
We consider the new divisor 253 and the new remainder 223,and apply the division lemma to get
253 = 223 x 1 + 30
We consider the new divisor 223 and the new remainder 30,and apply the division lemma to get
223 = 30 x 7 + 13
We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get
30 = 13 x 2 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 982 and 8585 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(223,30) = HCF(253,223) = HCF(729,253) = HCF(982,729) = HCF(8585,982) .
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Frequently Asked Questions on HCF of 982, 8585 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 982, 8585?
Answer: HCF of 982, 8585 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 982, 8585 using Euclid's Algorithm?
Answer: For arbitrary numbers 982, 8585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
