Highest Common Factor of 695, 960 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 695, 960 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 695, 960 is 5 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 695, 960 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 695, 960 is 5.
HCF(695, 960) = 5
HCF of 695, 960 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 695, 960 is 5.
Highest Common Factor of 695,960 is 5
Step 1: Since 960 > 695, we apply the division lemma to 960 and 695, to get
960 = 695 x 1 + 265
Step 2: Since the reminder 695 ≠ 0, we apply division lemma to 265 and 695, to get
695 = 265 x 2 + 165
Step 3: We consider the new divisor 265 and the new remainder 165, and apply the division lemma to get
265 = 165 x 1 + 100
We consider the new divisor 165 and the new remainder 100,and apply the division lemma to get
165 = 100 x 1 + 65
We consider the new divisor 100 and the new remainder 65,and apply the division lemma to get
100 = 65 x 1 + 35
We consider the new divisor 65 and the new remainder 35,and apply the division lemma to get
65 = 35 x 1 + 30
We consider the new divisor 35 and the new remainder 30,and apply the division lemma to get
35 = 30 x 1 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 695 and 960 is 5
Notice that 5 = HCF(30,5) = HCF(35,30) = HCF(65,35) = HCF(100,65) = HCF(165,100) = HCF(265,165) = HCF(695,265) = HCF(960,695) .
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Frequently Asked Questions on HCF of 695, 960 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 695, 960?
Answer: HCF of 695, 960 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 695, 960 using Euclid's Algorithm?
Answer: For arbitrary numbers 695, 960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.