Highest Common Factor of 577, 126, 878 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 577, 126, 878 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 577, 126, 878 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 577, 126, 878 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 577, 126, 878 is 1.
HCF(577, 126, 878) = 1
HCF of 577, 126, 878 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 577, 126, 878 is 1.
Highest Common Factor of 577,126,878 is 1
Step 1: Since 577 > 126, we apply the division lemma to 577 and 126, to get
577 = 126 x 4 + 73
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 73 and 126, to get
126 = 73 x 1 + 53
Step 3: We consider the new divisor 73 and the new remainder 53, and apply the division lemma to get
73 = 53 x 1 + 20
We consider the new divisor 53 and the new remainder 20,and apply the division lemma to get
53 = 20 x 2 + 13
We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get
20 = 13 x 1 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 577 and 126 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(53,20) = HCF(73,53) = HCF(126,73) = HCF(577,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 878 > 1, we apply the division lemma to 878 and 1, to get
878 = 1 x 878 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 878 is 1
Notice that 1 = HCF(878,1) .
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Frequently Asked Questions on HCF of 577, 126, 878 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 577, 126, 878?
Answer: HCF of 577, 126, 878 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 577, 126, 878 using Euclid's Algorithm?
Answer: For arbitrary numbers 577, 126, 878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.