Highest Common Factor of 112, 504, 728 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 112, 504, 728 i.e. 56 the largest integer that leaves a remainder zero for all numbers.
HCF of 112, 504, 728 is 56 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 112, 504, 728 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 112, 504, 728 is 56.
HCF(112, 504, 728) = 56
HCF of 112, 504, 728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 112, 504, 728 is 56.
Highest Common Factor of 112,504,728 is 56
Step 1: Since 504 > 112, we apply the division lemma to 504 and 112, to get
504 = 112 x 4 + 56
Step 2: Since the reminder 112 ≠ 0, we apply division lemma to 56 and 112, to get
112 = 56 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 56, the HCF of 112 and 504 is 56
Notice that 56 = HCF(112,56) = HCF(504,112) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 728 > 56, we apply the division lemma to 728 and 56, to get
728 = 56 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 56, the HCF of 56 and 728 is 56
Notice that 56 = HCF(728,56) .
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Frequently Asked Questions on HCF of 112, 504, 728 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 112, 504, 728?
Answer: HCF of 112, 504, 728 is 56 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 112, 504, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 112, 504, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.