Highest Common Factor of 565, 412, 578 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 565, 412, 578 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 412, 578 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 565, 412, 578 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 565, 412, 578 is 1.
HCF(565, 412, 578) = 1
HCF of 565, 412, 578 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 565, 412, 578 is 1.
Highest Common Factor of 565,412,578 is 1
Step 1: Since 565 > 412, we apply the division lemma to 565 and 412, to get
565 = 412 x 1 + 153
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 153 and 412, to get
412 = 153 x 2 + 106
Step 3: We consider the new divisor 153 and the new remainder 106, and apply the division lemma to get
153 = 106 x 1 + 47
We consider the new divisor 106 and the new remainder 47,and apply the division lemma to get
106 = 47 x 2 + 12
We consider the new divisor 47 and the new remainder 12,and apply the division lemma to get
47 = 12 x 3 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 565 and 412 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(47,12) = HCF(106,47) = HCF(153,106) = HCF(412,153) = HCF(565,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 578 > 1, we apply the division lemma to 578 and 1, to get
578 = 1 x 578 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 578 is 1
Notice that 1 = HCF(578,1) .
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Frequently Asked Questions on HCF of 565, 412, 578 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 565, 412, 578?
Answer: HCF of 565, 412, 578 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 412, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 412, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.