Highest Common Factor of 880, 546, 412 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 880, 546, 412 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 880, 546, 412 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 880, 546, 412 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 880, 546, 412 is 2.
HCF(880, 546, 412) = 2
HCF of 880, 546, 412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 880, 546, 412 is 2.
Highest Common Factor of 880,546,412 is 2
Step 1: Since 880 > 546, we apply the division lemma to 880 and 546, to get
880 = 546 x 1 + 334
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 334 and 546, to get
546 = 334 x 1 + 212
Step 3: We consider the new divisor 334 and the new remainder 212, and apply the division lemma to get
334 = 212 x 1 + 122
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 880 and 546 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(32,26) = HCF(90,32) = HCF(122,90) = HCF(212,122) = HCF(334,212) = HCF(546,334) = HCF(880,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 412 > 2, we apply the division lemma to 412 and 2, to get
412 = 2 x 206 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 412 is 2
Notice that 2 = HCF(412,2) .
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Frequently Asked Questions on HCF of 880, 546, 412 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 880, 546, 412?
Answer: HCF of 880, 546, 412 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 880, 546, 412 using Euclid's Algorithm?
Answer: For arbitrary numbers 880, 546, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.