Highest Common Factor of 914, 8998, 9786 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 914, 8998, 9786 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 914, 8998, 9786 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 914, 8998, 9786 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 914, 8998, 9786 is 2.
HCF(914, 8998, 9786) = 2
HCF of 914, 8998, 9786 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 914, 8998, 9786 is 2.
Highest Common Factor of 914,8998,9786 is 2
Step 1: Since 8998 > 914, we apply the division lemma to 8998 and 914, to get
8998 = 914 x 9 + 772
Step 2: Since the reminder 914 ≠ 0, we apply division lemma to 772 and 914, to get
914 = 772 x 1 + 142
Step 3: We consider the new divisor 772 and the new remainder 142, and apply the division lemma to get
772 = 142 x 5 + 62
We consider the new divisor 142 and the new remainder 62,and apply the division lemma to get
142 = 62 x 2 + 18
We consider the new divisor 62 and the new remainder 18,and apply the division lemma to get
62 = 18 x 3 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 914 and 8998 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(62,18) = HCF(142,62) = HCF(772,142) = HCF(914,772) = HCF(8998,914) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9786 > 2, we apply the division lemma to 9786 and 2, to get
9786 = 2 x 4893 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9786 is 2
Notice that 2 = HCF(9786,2) .
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Frequently Asked Questions on HCF of 914, 8998, 9786 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 914, 8998, 9786?
Answer: HCF of 914, 8998, 9786 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 914, 8998, 9786 using Euclid's Algorithm?
Answer: For arbitrary numbers 914, 8998, 9786 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.