Highest Common Factor of 982, 413, 105 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, 413, 105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 982, 413, 105 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, 413, 105 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, 413, 105 is 1.
HCF(982, 413, 105) = 1
HCF of 982, 413, 105 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, 413, 105 is 1.
Highest Common Factor of 982,413,105 is 1
Step 1: Since 982 > 413, we apply the division lemma to 982 and 413, to get
982 = 413 x 2 + 156
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 156 and 413, to get
413 = 156 x 2 + 101
Step 3: We consider the new divisor 156 and the new remainder 101, and apply the division lemma to get
156 = 101 x 1 + 55
We consider the new divisor 101 and the new remainder 55,and apply the division lemma to get
101 = 55 x 1 + 46
We consider the new divisor 55 and the new remainder 46,and apply the division lemma to get
55 = 46 x 1 + 9
We consider the new divisor 46 and the new remainder 9,and apply the division lemma to get
46 = 9 x 5 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 982 and 413 is 1
Notice that 1 = HCF(9,1) = HCF(46,9) = HCF(55,46) = HCF(101,55) = HCF(156,101) = HCF(413,156) = HCF(982,413) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get
105 = 1 x 105 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1
Notice that 1 = HCF(105,1) .
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Frequently Asked Questions on HCF of 982, 413, 105 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, 413, 105?
Answer: HCF of 982, 413, 105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 982, 413, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 982, 413, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.