Highest Common Factor of 410, 649 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, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 649 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 410, 649 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, 649 is 1.
HCF(410, 649) = 1
HCF of 410, 649 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, 649 is 1.
Highest Common Factor of 410,649 is 1
Step 1: Since 649 > 410, we apply the division lemma to 649 and 410, to get
649 = 410 x 1 + 239
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 239 and 410, to get
410 = 239 x 1 + 171
Step 3: We consider the new divisor 239 and the new remainder 171, and apply the division lemma to get
239 = 171 x 1 + 68
We consider the new divisor 171 and the new remainder 68,and apply the division lemma to get
171 = 68 x 2 + 35
We consider the new divisor 68 and the new remainder 35,and apply the division lemma to get
68 = 35 x 1 + 33
We consider the new divisor 35 and the new remainder 33,and apply the division lemma to get
35 = 33 x 1 + 2
We consider the new divisor 33 and the new remainder 2,and apply the division lemma to get
33 = 2 x 16 + 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 410 and 649 is 1
Notice that 1 = HCF(2,1) = HCF(33,2) = HCF(35,33) = HCF(68,35) = HCF(171,68) = HCF(239,171) = HCF(410,239) = HCF(649,410) .
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Frequently Asked Questions on HCF of 410, 649 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, 649?
Answer: HCF of 410, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 649 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.