Highest Common Factor of 984, 217 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 984, 217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 984, 217 is 1 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 984, 217 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 984, 217 is 1.
HCF(984, 217) = 1
HCF of 984, 217 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 984, 217 is 1.
Highest Common Factor of 984,217 is 1
Step 1: Since 984 > 217, we apply the division lemma to 984 and 217, to get
984 = 217 x 4 + 116
Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 116 and 217, to get
217 = 116 x 1 + 101
Step 3: We consider the new divisor 116 and the new remainder 101, and apply the division lemma to get
116 = 101 x 1 + 15
We consider the new divisor 101 and the new remainder 15,and apply the division lemma to get
101 = 15 x 6 + 11
We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get
15 = 11 x 1 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 984 and 217 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(101,15) = HCF(116,101) = HCF(217,116) = HCF(984,217) .
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Frequently Asked Questions on HCF of 984, 217 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 984, 217?
Answer: HCF of 984, 217 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 984, 217 using Euclid's Algorithm?
Answer: For arbitrary numbers 984, 217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.