Highest Common Factor of 546, 369, 23 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, 369, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 369, 23 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 546, 369, 23 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, 369, 23 is 1.
HCF(546, 369, 23) = 1
HCF of 546, 369, 23 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, 369, 23 is 1.
Highest Common Factor of 546,369,23 is 1
Step 1: Since 546 > 369, we apply the division lemma to 546 and 369, to get
546 = 369 x 1 + 177
Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 177 and 369, to get
369 = 177 x 2 + 15
Step 3: We consider the new divisor 177 and the new remainder 15, and apply the division lemma to get
177 = 15 x 11 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 546 and 369 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(177,15) = HCF(369,177) = HCF(546,369) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 23 > 3, we apply the division lemma to 23 and 3, to get
23 = 3 x 7 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 23 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) .
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Frequently Asked Questions on HCF of 546, 369, 23 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, 369, 23?
Answer: HCF of 546, 369, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 369, 23 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 369, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.