Highest Common Factor of 410, 8468 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 410, 8468 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 8468 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 410, 8468 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 410, 8468 is 2.
HCF(410, 8468) = 2
HCF of 410, 8468 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 410, 8468 is 2.
Highest Common Factor of 410,8468 is 2
Step 1: Since 8468 > 410, we apply the division lemma to 8468 and 410, to get
8468 = 410 x 20 + 268
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 268 and 410, to get
410 = 268 x 1 + 142
Step 3: We consider the new divisor 268 and the new remainder 142, and apply the division lemma to get
268 = 142 x 1 + 126
We consider the new divisor 142 and the new remainder 126,and apply the division lemma to get
142 = 126 x 1 + 16
We consider the new divisor 126 and the new remainder 16,and apply the division lemma to get
126 = 16 x 7 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 410 and 8468 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(126,16) = HCF(142,126) = HCF(268,142) = HCF(410,268) = HCF(8468,410) .
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Frequently Asked Questions on HCF of 410, 8468 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 410, 8468?
Answer: HCF of 410, 8468 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 8468 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 8468 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.