Highest Common Factor of 545, 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 545, 878 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 545, 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 545, 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 545, 878 is 1.
HCF(545, 878) = 1
HCF of 545, 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 545, 878 is 1.
Highest Common Factor of 545,878 is 1
Step 1: Since 878 > 545, we apply the division lemma to 878 and 545, to get
878 = 545 x 1 + 333
Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 333 and 545, to get
545 = 333 x 1 + 212
Step 3: We consider the new divisor 333 and the new remainder 212, and apply the division lemma to get
333 = 212 x 1 + 121
We consider the new divisor 212 and the new remainder 121,and apply the division lemma to get
212 = 121 x 1 + 91
We consider the new divisor 121 and the new remainder 91,and apply the division lemma to get
121 = 91 x 1 + 30
We consider the new divisor 91 and the new remainder 30,and apply the division lemma to get
91 = 30 x 3 + 1
We consider the new divisor 30 and the new remainder 1,and apply the division lemma to get
30 = 1 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 545 and 878 is 1
Notice that 1 = HCF(30,1) = HCF(91,30) = HCF(121,91) = HCF(212,121) = HCF(333,212) = HCF(545,333) = HCF(878,545) .
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Frequently Asked Questions on HCF of 545, 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 545, 878?
Answer: HCF of 545, 878 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 545, 878 using Euclid's Algorithm?
Answer: For arbitrary numbers 545, 878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.