Highest Common Factor of 116, 784, 922 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 116, 784, 922 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 116, 784, 922 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 116, 784, 922 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 116, 784, 922 is 2.
HCF(116, 784, 922) = 2
HCF of 116, 784, 922 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 116, 784, 922 is 2.
Highest Common Factor of 116,784,922 is 2
Step 1: Since 784 > 116, we apply the division lemma to 784 and 116, to get
784 = 116 x 6 + 88
Step 2: Since the reminder 116 ≠ 0, we apply division lemma to 88 and 116, to get
116 = 88 x 1 + 28
Step 3: We consider the new divisor 88 and the new remainder 28, and apply the division lemma to get
88 = 28 x 3 + 4
We consider the new divisor 28 and the new remainder 4, and apply the division lemma to get
28 = 4 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 116 and 784 is 4
Notice that 4 = HCF(28,4) = HCF(88,28) = HCF(116,88) = HCF(784,116) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 922 > 4, we apply the division lemma to 922 and 4, to get
922 = 4 x 230 + 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 922 is 2
Notice that 2 = HCF(4,2) = HCF(922,4) .
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Frequently Asked Questions on HCF of 116, 784, 922 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 116, 784, 922?
Answer: HCF of 116, 784, 922 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 116, 784, 922 using Euclid's Algorithm?
Answer: For arbitrary numbers 116, 784, 922 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.