Highest Common Factor of 410, 945, 205 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, 945, 205 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 945, 205 is 5 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, 945, 205 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, 945, 205 is 5.
HCF(410, 945, 205) = 5
HCF of 410, 945, 205 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, 945, 205 is 5.
Highest Common Factor of 410,945,205 is 5
Step 1: Since 945 > 410, we apply the division lemma to 945 and 410, to get
945 = 410 x 2 + 125
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 125 and 410, to get
410 = 125 x 3 + 35
Step 3: We consider the new divisor 125 and the new remainder 35, and apply the division lemma to get
125 = 35 x 3 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 410 and 945 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(125,35) = HCF(410,125) = HCF(945,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 205 > 5, we apply the division lemma to 205 and 5, to get
205 = 5 x 41 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 205 is 5
Notice that 5 = HCF(205,5) .
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Frequently Asked Questions on HCF of 410, 945, 205 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, 945, 205?
Answer: HCF of 410, 945, 205 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 945, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 945, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.