Highest Common Factor of 546, 728, 112 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, 728, 112 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 728, 112 is 14 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, 728, 112 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, 728, 112 is 14.
HCF(546, 728, 112) = 14
HCF of 546, 728, 112 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, 728, 112 is 14.
Highest Common Factor of 546,728,112 is 14
Step 1: Since 728 > 546, we apply the division lemma to 728 and 546, to get
728 = 546 x 1 + 182
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 182 and 546, to get
546 = 182 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 182, the HCF of 546 and 728 is 182
Notice that 182 = HCF(546,182) = HCF(728,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 182 > 112, we apply the division lemma to 182 and 112, to get
182 = 112 x 1 + 70
Step 2: Since the reminder 112 ≠ 0, we apply division lemma to 70 and 112, to get
112 = 70 x 1 + 42
Step 3: We consider the new divisor 70 and the new remainder 42, and apply the division lemma to get
70 = 42 x 1 + 28
We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get
42 = 28 x 1 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 182 and 112 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(70,42) = HCF(112,70) = HCF(182,112) .
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Frequently Asked Questions on HCF of 546, 728, 112 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, 728, 112?
Answer: HCF of 546, 728, 112 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 728, 112 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 728, 112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.