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 727, 408, 866 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 727, 408, 866 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 727, 408, 866 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 727, 408, 866 is 1.
HCF(727, 408, 866) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 727, 408, 866 is 1.
Step 1: Since 727 > 408, we apply the division lemma to 727 and 408, to get
727 = 408 x 1 + 319
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 319 and 408, to get
408 = 319 x 1 + 89
Step 3: We consider the new divisor 319 and the new remainder 89, and apply the division lemma to get
319 = 89 x 3 + 52
We consider the new divisor 89 and the new remainder 52,and apply the division lemma to get
89 = 52 x 1 + 37
We consider the new divisor 52 and the new remainder 37,and apply the division lemma to get
52 = 37 x 1 + 15
We consider the new divisor 37 and the new remainder 15,and apply the division lemma to get
37 = 15 x 2 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 727 and 408 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(37,15) = HCF(52,37) = HCF(89,52) = HCF(319,89) = HCF(408,319) = HCF(727,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 866 > 1, we apply the division lemma to 866 and 1, to get
866 = 1 x 866 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 866 is 1
Notice that 1 = HCF(866,1) .
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 727, 408, 866?
Answer: HCF of 727, 408, 866 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 727, 408, 866 using Euclid's Algorithm?
Answer: For arbitrary numbers 727, 408, 866 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.