Highest Common Factor of 440, 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 440, 728 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 440, 728 is 8 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 440, 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 440, 728 is 8.
HCF(440, 728) = 8
HCF of 440, 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 440, 728 is 8.
Highest Common Factor of 440,728 is 8
Step 1: Since 728 > 440, we apply the division lemma to 728 and 440, to get
728 = 440 x 1 + 288
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 288 and 440, to get
440 = 288 x 1 + 152
Step 3: We consider the new divisor 288 and the new remainder 152, and apply the division lemma to get
288 = 152 x 1 + 136
We consider the new divisor 152 and the new remainder 136,and apply the division lemma to get
152 = 136 x 1 + 16
We consider the new divisor 136 and the new remainder 16,and apply the division lemma to get
136 = 16 x 8 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 440 and 728 is 8
Notice that 8 = HCF(16,8) = HCF(136,16) = HCF(152,136) = HCF(288,152) = HCF(440,288) = HCF(728,440) .
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Frequently Asked Questions on HCF of 440, 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 440, 728?
Answer: HCF of 440, 728 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 440, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 440, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.