Highest Common Factor of 813, 9240, 8709 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 813, 9240, 8709 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 813, 9240, 8709 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 813, 9240, 8709 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 813, 9240, 8709 is 3.
HCF(813, 9240, 8709) = 3
HCF of 813, 9240, 8709 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 813, 9240, 8709 is 3.
Highest Common Factor of 813,9240,8709 is 3
Step 1: Since 9240 > 813, we apply the division lemma to 9240 and 813, to get
9240 = 813 x 11 + 297
Step 2: Since the reminder 813 ≠ 0, we apply division lemma to 297 and 813, to get
813 = 297 x 2 + 219
Step 3: We consider the new divisor 297 and the new remainder 219, and apply the division lemma to get
297 = 219 x 1 + 78
We consider the new divisor 219 and the new remainder 78,and apply the division lemma to get
219 = 78 x 2 + 63
We consider the new divisor 78 and the new remainder 63,and apply the division lemma to get
78 = 63 x 1 + 15
We consider the new divisor 63 and the new remainder 15,and apply the division lemma to get
63 = 15 x 4 + 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 813 and 9240 is 3
Notice that 3 = HCF(15,3) = HCF(63,15) = HCF(78,63) = HCF(219,78) = HCF(297,219) = HCF(813,297) = HCF(9240,813) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8709 > 3, we apply the division lemma to 8709 and 3, to get
8709 = 3 x 2903 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 8709 is 3
Notice that 3 = HCF(8709,3) .
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Frequently Asked Questions on HCF of 813, 9240, 8709 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 813, 9240, 8709?
Answer: HCF of 813, 9240, 8709 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 813, 9240, 8709 using Euclid's Algorithm?
Answer: For arbitrary numbers 813, 9240, 8709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
