Highest Common Factor of 5728, 8384 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 5728, 8384 i.e. 32 the largest integer that leaves a remainder zero for all numbers.
HCF of 5728, 8384 is 32 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 5728, 8384 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 5728, 8384 is 32.
HCF(5728, 8384) = 32
HCF of 5728, 8384 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5728, 8384 is 32.
Highest Common Factor of 5728,8384 is 32
Step 1: Since 8384 > 5728, we apply the division lemma to 8384 and 5728, to get
8384 = 5728 x 1 + 2656
Step 2: Since the reminder 5728 ≠ 0, we apply division lemma to 2656 and 5728, to get
5728 = 2656 x 2 + 416
Step 3: We consider the new divisor 2656 and the new remainder 416, and apply the division lemma to get
2656 = 416 x 6 + 160
We consider the new divisor 416 and the new remainder 160,and apply the division lemma to get
416 = 160 x 2 + 96
We consider the new divisor 160 and the new remainder 96,and apply the division lemma to get
160 = 96 x 1 + 64
We consider the new divisor 96 and the new remainder 64,and apply the division lemma to get
96 = 64 x 1 + 32
We consider the new divisor 64 and the new remainder 32,and apply the division lemma to get
64 = 32 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 5728 and 8384 is 32
Notice that 32 = HCF(64,32) = HCF(96,64) = HCF(160,96) = HCF(416,160) = HCF(2656,416) = HCF(5728,2656) = HCF(8384,5728) .
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Frequently Asked Questions on HCF of 5728, 8384 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 5728, 8384?
Answer: HCF of 5728, 8384 is 32 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5728, 8384 using Euclid's Algorithm?
Answer: For arbitrary numbers 5728, 8384 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.