Highest Common Factor of 578, 739, 577 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 578, 739, 577 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 739, 577 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 578, 739, 577 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 578, 739, 577 is 1.
HCF(578, 739, 577) = 1
HCF of 578, 739, 577 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 578, 739, 577 is 1.
Highest Common Factor of 578,739,577 is 1
Step 1: Since 739 > 578, we apply the division lemma to 739 and 578, to get
739 = 578 x 1 + 161
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 161 and 578, to get
578 = 161 x 3 + 95
Step 3: We consider the new divisor 161 and the new remainder 95, and apply the division lemma to get
161 = 95 x 1 + 66
We consider the new divisor 95 and the new remainder 66,and apply the division lemma to get
95 = 66 x 1 + 29
We consider the new divisor 66 and the new remainder 29,and apply the division lemma to get
66 = 29 x 2 + 8
We consider the new divisor 29 and the new remainder 8,and apply the division lemma to get
29 = 8 x 3 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 578 and 739 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(66,29) = HCF(95,66) = HCF(161,95) = HCF(578,161) = HCF(739,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 577 > 1, we apply the division lemma to 577 and 1, to get
577 = 1 x 577 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 577 is 1
Notice that 1 = HCF(577,1) .
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Frequently Asked Questions on HCF of 578, 739, 577 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 578, 739, 577?
Answer: HCF of 578, 739, 577 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 739, 577 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 739, 577 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
