Highest Common Factor of 409, 10482 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 409, 10482 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 409, 10482 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 409, 10482 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 409, 10482 is 1.
HCF(409, 10482) = 1
HCF of 409, 10482 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 409, 10482 is 1.
Highest Common Factor of 409,10482 is 1
Step 1: Since 10482 > 409, we apply the division lemma to 10482 and 409, to get
10482 = 409 x 25 + 257
Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 257 and 409, to get
409 = 257 x 1 + 152
Step 3: We consider the new divisor 257 and the new remainder 152, and apply the division lemma to get
257 = 152 x 1 + 105
We consider the new divisor 152 and the new remainder 105,and apply the division lemma to get
152 = 105 x 1 + 47
We consider the new divisor 105 and the new remainder 47,and apply the division lemma to get
105 = 47 x 2 + 11
We consider the new divisor 47 and the new remainder 11,and apply the division lemma to get
47 = 11 x 4 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 409 and 10482 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(47,11) = HCF(105,47) = HCF(152,105) = HCF(257,152) = HCF(409,257) = HCF(10482,409) .
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Frequently Asked Questions on HCF of 409, 10482 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 409, 10482?
Answer: HCF of 409, 10482 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 409, 10482 using Euclid's Algorithm?
Answer: For arbitrary numbers 409, 10482 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.