Highest Common Factor of 687, 441, 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 687, 441, 696 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 441, 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 687, 441, 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 687, 441, 696 is 3.
HCF(687, 441, 696) = 3
HCF of 687, 441, 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 687, 441, 696 is 3.
Highest Common Factor of 687,441,696 is 3
Step 1: Since 687 > 441, we apply the division lemma to 687 and 441, to get
687 = 441 x 1 + 246
Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 246 and 441, to get
441 = 246 x 1 + 195
Step 3: We consider the new divisor 246 and the new remainder 195, and apply the division lemma to get
246 = 195 x 1 + 51
We consider the new divisor 195 and the new remainder 51,and apply the division lemma to get
195 = 51 x 3 + 42
We consider the new divisor 51 and the new remainder 42,and apply the division lemma to get
51 = 42 x 1 + 9
We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get
42 = 9 x 4 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 687 and 441 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(51,42) = HCF(195,51) = HCF(246,195) = HCF(441,246) = HCF(687,441) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 696 > 3, we apply the division lemma to 696 and 3, to get
696 = 3 x 232 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 696 is 3
Notice that 3 = HCF(696,3) .
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Frequently Asked Questions on HCF of 687, 441, 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 687, 441, 696?
Answer: HCF of 687, 441, 696 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 441, 696 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 441, 696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.