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, 879, 395 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 879, 395 is 1 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, 879, 395 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, 879, 395 is 1.
HCF(687, 879, 395) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 879, 395 is 1.
Step 1: Since 879 > 687, we apply the division lemma to 879 and 687, to get
879 = 687 x 1 + 192
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 192 and 687, to get
687 = 192 x 3 + 111
Step 3: We consider the new divisor 192 and the new remainder 111, and apply the division lemma to get
192 = 111 x 1 + 81
We consider the new divisor 111 and the new remainder 81,and apply the division lemma to get
111 = 81 x 1 + 30
We consider the new divisor 81 and the new remainder 30,and apply the division lemma to get
81 = 30 x 2 + 21
We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get
30 = 21 x 1 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 687 and 879 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(81,30) = HCF(111,81) = HCF(192,111) = HCF(687,192) = HCF(879,687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 395 > 3, we apply the division lemma to 395 and 3, to get
395 = 3 x 131 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 395 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(395,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 879, 395?
Answer: HCF of 687, 879, 395 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 879, 395 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 879, 395 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.