Highest Common Factor of 410, 628 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, 628 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 628 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, 628 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, 628 is 2.
HCF(410, 628) = 2
HCF of 410, 628 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, 628 is 2.
Highest Common Factor of 410,628 is 2
Step 1: Since 628 > 410, we apply the division lemma to 628 and 410, to get
628 = 410 x 1 + 218
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 218 and 410, to get
410 = 218 x 1 + 192
Step 3: We consider the new divisor 218 and the new remainder 192, and apply the division lemma to get
218 = 192 x 1 + 26
We consider the new divisor 192 and the new remainder 26,and apply the division lemma to get
192 = 26 x 7 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 410 and 628 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(192,26) = HCF(218,192) = HCF(410,218) = HCF(628,410) .
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Frequently Asked Questions on HCF of 410, 628 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, 628?
Answer: HCF of 410, 628 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 628 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 628 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.