Highest Common Factor of 784, 6888, 2696 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, 6888, 2696 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 6888, 2696 is 8 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, 6888, 2696 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, 6888, 2696 is 8.
HCF(784, 6888, 2696) = 8
HCF of 784, 6888, 2696 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, 6888, 2696 is 8.
Highest Common Factor of 784,6888,2696 is 8
Step 1: Since 6888 > 784, we apply the division lemma to 6888 and 784, to get
6888 = 784 x 8 + 616
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 616 and 784, to get
784 = 616 x 1 + 168
Step 3: We consider the new divisor 616 and the new remainder 168, and apply the division lemma to get
616 = 168 x 3 + 112
We consider the new divisor 168 and the new remainder 112,and apply the division lemma to get
168 = 112 x 1 + 56
We consider the new divisor 112 and the new remainder 56,and apply the division lemma to get
112 = 56 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 56, the HCF of 784 and 6888 is 56
Notice that 56 = HCF(112,56) = HCF(168,112) = HCF(616,168) = HCF(784,616) = HCF(6888,784) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2696 > 56, we apply the division lemma to 2696 and 56, to get
2696 = 56 x 48 + 8
Step 2: Since the reminder 56 ≠ 0, we apply division lemma to 8 and 56, to get
56 = 8 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 56 and 2696 is 8
Notice that 8 = HCF(56,8) = HCF(2696,56) .
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Frequently Asked Questions on HCF of 784, 6888, 2696 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, 6888, 2696?
Answer: HCF of 784, 6888, 2696 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 6888, 2696 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 6888, 2696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
