Highest Common Factor of 412, 521, 96 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 412, 521, 96 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 521, 96 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 412, 521, 96 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 412, 521, 96 is 1.
HCF(412, 521, 96) = 1
HCF of 412, 521, 96 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 521, 96 is 1.
Highest Common Factor of 412,521,96 is 1
Step 1: Since 521 > 412, we apply the division lemma to 521 and 412, to get
521 = 412 x 1 + 109
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 109 and 412, to get
412 = 109 x 3 + 85
Step 3: We consider the new divisor 109 and the new remainder 85, and apply the division lemma to get
109 = 85 x 1 + 24
We consider the new divisor 85 and the new remainder 24,and apply the division lemma to get
85 = 24 x 3 + 13
We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get
24 = 13 x 1 + 11
We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get
13 = 11 x 1 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 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 412 and 521 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(85,24) = HCF(109,85) = HCF(412,109) = HCF(521,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 96 > 1, we apply the division lemma to 96 and 1, to get
96 = 1 x 96 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 96 is 1
Notice that 1 = HCF(96,1) .
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Frequently Asked Questions on HCF of 412, 521, 96 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 412, 521, 96?
Answer: HCF of 412, 521, 96 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 521, 96 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 521, 96 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
