Highest Common Factor of 474, 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 474, 728 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 474, 728 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 474, 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 474, 728 is 2.
HCF(474, 728) = 2
HCF of 474, 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 474, 728 is 2.
Highest Common Factor of 474,728 is 2
Step 1: Since 728 > 474, we apply the division lemma to 728 and 474, to get
728 = 474 x 1 + 254
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 254 and 474, to get
474 = 254 x 1 + 220
Step 3: We consider the new divisor 254 and the new remainder 220, and apply the division lemma to get
254 = 220 x 1 + 34
We consider the new divisor 220 and the new remainder 34,and apply the division lemma to get
220 = 34 x 6 + 16
We consider the new divisor 34 and the new remainder 16,and apply the division lemma to get
34 = 16 x 2 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 474 and 728 is 2
Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(220,34) = HCF(254,220) = HCF(474,254) = HCF(728,474) .
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Frequently Asked Questions on HCF of 474, 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 474, 728?
Answer: HCF of 474, 728 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 474, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 474, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.