Highest Common Factor of 546, 758, 406 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, 758, 406 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 758, 406 is 2 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, 758, 406 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, 758, 406 is 2.
HCF(546, 758, 406) = 2
HCF of 546, 758, 406 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, 758, 406 is 2.
Highest Common Factor of 546,758,406 is 2
Step 1: Since 758 > 546, we apply the division lemma to 758 and 546, to get
758 = 546 x 1 + 212
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 212 and 546, to get
546 = 212 x 2 + 122
Step 3: We consider the new divisor 212 and the new remainder 122, and apply the division lemma to get
212 = 122 x 1 + 90
We consider the new divisor 122 and the new remainder 90,and apply the division lemma to get
122 = 90 x 1 + 32
We consider the new divisor 90 and the new remainder 32,and apply the division lemma to get
90 = 32 x 2 + 26
We consider the new divisor 32 and the new remainder 26,and apply the division lemma to get
32 = 26 x 1 + 6
We consider the new divisor 26 and the new remainder 6,and apply the division lemma to get
26 = 6 x 4 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 546 and 758 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(32,26) = HCF(90,32) = HCF(122,90) = HCF(212,122) = HCF(546,212) = HCF(758,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 406 > 2, we apply the division lemma to 406 and 2, to get
406 = 2 x 203 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 406 is 2
Notice that 2 = HCF(406,2) .
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Frequently Asked Questions on HCF of 546, 758, 406 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, 758, 406?
Answer: HCF of 546, 758, 406 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 758, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 758, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.