Highest Common Factor of 546, 885, 54 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 546, 885, 54 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 885, 54 is 3 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 546, 885, 54 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 546, 885, 54 is 3.
HCF(546, 885, 54) = 3
HCF of 546, 885, 54 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 546, 885, 54 is 3.
Highest Common Factor of 546,885,54 is 3
Step 1: Since 885 > 546, we apply the division lemma to 885 and 546, to get
885 = 546 x 1 + 339
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 339 and 546, to get
546 = 339 x 1 + 207
Step 3: We consider the new divisor 339 and the new remainder 207, and apply the division lemma to get
339 = 207 x 1 + 132
We consider the new divisor 207 and the new remainder 132,and apply the division lemma to get
207 = 132 x 1 + 75
We consider the new divisor 132 and the new remainder 75,and apply the division lemma to get
132 = 75 x 1 + 57
We consider the new divisor 75 and the new remainder 57,and apply the division lemma to get
75 = 57 x 1 + 18
We consider the new divisor 57 and the new remainder 18,and apply the division lemma to get
57 = 18 x 3 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 546 and 885 is 3
Notice that 3 = HCF(18,3) = HCF(57,18) = HCF(75,57) = HCF(132,75) = HCF(207,132) = HCF(339,207) = HCF(546,339) = HCF(885,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 3, we apply the division lemma to 54 and 3, to get
54 = 3 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 54 is 3
Notice that 3 = HCF(54,3) .
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Frequently Asked Questions on HCF of 546, 885, 54 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 546, 885, 54?
Answer: HCF of 546, 885, 54 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 885, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 885, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.