Highest Common Factor of 784, 8300, 2762 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 784, 8300, 2762 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 8300, 2762 is 2 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 784, 8300, 2762 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 784, 8300, 2762 is 2.
HCF(784, 8300, 2762) = 2
HCF of 784, 8300, 2762 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 784, 8300, 2762 is 2.
Highest Common Factor of 784,8300,2762 is 2
Step 1: Since 8300 > 784, we apply the division lemma to 8300 and 784, to get
8300 = 784 x 10 + 460
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 460 and 784, to get
784 = 460 x 1 + 324
Step 3: We consider the new divisor 460 and the new remainder 324, and apply the division lemma to get
460 = 324 x 1 + 136
We consider the new divisor 324 and the new remainder 136,and apply the division lemma to get
324 = 136 x 2 + 52
We consider the new divisor 136 and the new remainder 52,and apply the division lemma to get
136 = 52 x 2 + 32
We consider the new divisor 52 and the new remainder 32,and apply the division lemma to get
52 = 32 x 1 + 20
We consider the new divisor 32 and the new remainder 20,and apply the division lemma to get
32 = 20 x 1 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 784 and 8300 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(52,32) = HCF(136,52) = HCF(324,136) = HCF(460,324) = HCF(784,460) = HCF(8300,784) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2762 > 4, we apply the division lemma to 2762 and 4, to get
2762 = 4 x 690 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 2762 is 2
Notice that 2 = HCF(4,2) = HCF(2762,4) .
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Frequently Asked Questions on HCF of 784, 8300, 2762 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 784, 8300, 2762?
Answer: HCF of 784, 8300, 2762 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 8300, 2762 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 8300, 2762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.