Highest Common Factor of 255, 696 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 255, 696 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 255, 696 is 3 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 255, 696 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 255, 696 is 3.
HCF(255, 696) = 3
HCF of 255, 696 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 255, 696 is 3.
Highest Common Factor of 255,696 is 3
Step 1: Since 696 > 255, we apply the division lemma to 696 and 255, to get
696 = 255 x 2 + 186
Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 186 and 255, to get
255 = 186 x 1 + 69
Step 3: We consider the new divisor 186 and the new remainder 69, and apply the division lemma to get
186 = 69 x 2 + 48
We consider the new divisor 69 and the new remainder 48,and apply the division lemma to get
69 = 48 x 1 + 21
We consider the new divisor 48 and the new remainder 21,and apply the division lemma to get
48 = 21 x 2 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 255 and 696 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(48,21) = HCF(69,48) = HCF(186,69) = HCF(255,186) = HCF(696,255) .
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Frequently Asked Questions on HCF of 255, 696 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 255, 696?
Answer: HCF of 255, 696 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 255, 696 using Euclid's Algorithm?
Answer: For arbitrary numbers 255, 696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.