Highest Common Factor of 896, 665 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 896, 665 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 896, 665 is 7 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 896, 665 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 896, 665 is 7.
HCF(896, 665) = 7
HCF of 896, 665 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 896, 665 is 7.
Highest Common Factor of 896,665 is 7
Step 1: Since 896 > 665, we apply the division lemma to 896 and 665, to get
896 = 665 x 1 + 231
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 231 and 665, to get
665 = 231 x 2 + 203
Step 3: We consider the new divisor 231 and the new remainder 203, and apply the division lemma to get
231 = 203 x 1 + 28
We consider the new divisor 203 and the new remainder 28,and apply the division lemma to get
203 = 28 x 7 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 896 and 665 is 7
Notice that 7 = HCF(28,7) = HCF(203,28) = HCF(231,203) = HCF(665,231) = HCF(896,665) .
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Frequently Asked Questions on HCF of 896, 665 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 896, 665?
Answer: HCF of 896, 665 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 896, 665 using Euclid's Algorithm?
Answer: For arbitrary numbers 896, 665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.