Highest Common Factor of 728, 446 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 728, 446 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 446 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 728, 446 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 728, 446 is 2.
HCF(728, 446) = 2
HCF of 728, 446 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 446 is 2.
Highest Common Factor of 728,446 is 2
Step 1: Since 728 > 446, we apply the division lemma to 728 and 446, to get
728 = 446 x 1 + 282
Step 2: Since the reminder 446 ≠ 0, we apply division lemma to 282 and 446, to get
446 = 282 x 1 + 164
Step 3: We consider the new divisor 282 and the new remainder 164, and apply the division lemma to get
282 = 164 x 1 + 118
We consider the new divisor 164 and the new remainder 118,and apply the division lemma to get
164 = 118 x 1 + 46
We consider the new divisor 118 and the new remainder 46,and apply the division lemma to get
118 = 46 x 2 + 26
We consider the new divisor 46 and the new remainder 26,and apply the division lemma to get
46 = 26 x 1 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 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 728 and 446 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(46,26) = HCF(118,46) = HCF(164,118) = HCF(282,164) = HCF(446,282) = HCF(728,446) .
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Frequently Asked Questions on HCF of 728, 446 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 728, 446?
Answer: HCF of 728, 446 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 446 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 446 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.