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 879, 693, 405 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 879, 693, 405 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 879, 693, 405 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 879, 693, 405 is 3.
HCF(879, 693, 405) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 879, 693, 405 is 3.
Step 1: Since 879 > 693, we apply the division lemma to 879 and 693, to get
879 = 693 x 1 + 186
Step 2: Since the reminder 693 ≠ 0, we apply division lemma to 186 and 693, to get
693 = 186 x 3 + 135
Step 3: We consider the new divisor 186 and the new remainder 135, and apply the division lemma to get
186 = 135 x 1 + 51
We consider the new divisor 135 and the new remainder 51,and apply the division lemma to get
135 = 51 x 2 + 33
We consider the new divisor 51 and the new remainder 33,and apply the division lemma to get
51 = 33 x 1 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 879 and 693 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) = HCF(135,51) = HCF(186,135) = HCF(693,186) = HCF(879,693) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 405 > 3, we apply the division lemma to 405 and 3, to get
405 = 3 x 135 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 405 is 3
Notice that 3 = HCF(405,3) .
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 879, 693, 405?
Answer: HCF of 879, 693, 405 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 879, 693, 405 using Euclid's Algorithm?
Answer: For arbitrary numbers 879, 693, 405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.