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 826, 8711, 9213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 826, 8711, 9213 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 826, 8711, 9213 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 826, 8711, 9213 is 1.
HCF(826, 8711, 9213) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 826, 8711, 9213 is 1.
Step 1: Since 8711 > 826, we apply the division lemma to 8711 and 826, to get
8711 = 826 x 10 + 451
Step 2: Since the reminder 826 ≠ 0, we apply division lemma to 451 and 826, to get
826 = 451 x 1 + 375
Step 3: We consider the new divisor 451 and the new remainder 375, and apply the division lemma to get
451 = 375 x 1 + 76
We consider the new divisor 375 and the new remainder 76,and apply the division lemma to get
375 = 76 x 4 + 71
We consider the new divisor 76 and the new remainder 71,and apply the division lemma to get
76 = 71 x 1 + 5
We consider the new divisor 71 and the new remainder 5,and apply the division lemma to get
71 = 5 x 14 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 826 and 8711 is 1
Notice that 1 = HCF(5,1) = HCF(71,5) = HCF(76,71) = HCF(375,76) = HCF(451,375) = HCF(826,451) = HCF(8711,826) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9213 > 1, we apply the division lemma to 9213 and 1, to get
9213 = 1 x 9213 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9213 is 1
Notice that 1 = HCF(9213,1) .
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 826, 8711, 9213?
Answer: HCF of 826, 8711, 9213 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 826, 8711, 9213 using Euclid's Algorithm?
Answer: For arbitrary numbers 826, 8711, 9213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.