Highest Common Factor of 984, 8746 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, 8746 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 984, 8746 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 984, 8746 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, 8746 is 2.
HCF(984, 8746) = 2
HCF of 984, 8746 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, 8746 is 2.
Highest Common Factor of 984,8746 is 2
Step 1: Since 8746 > 984, we apply the division lemma to 8746 and 984, to get
8746 = 984 x 8 + 874
Step 2: Since the reminder 984 ≠ 0, we apply division lemma to 874 and 984, to get
984 = 874 x 1 + 110
Step 3: We consider the new divisor 874 and the new remainder 110, and apply the division lemma to get
874 = 110 x 7 + 104
We consider the new divisor 110 and the new remainder 104,and apply the division lemma to get
110 = 104 x 1 + 6
We consider the new divisor 104 and the new remainder 6,and apply the division lemma to get
104 = 6 x 17 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 984 and 8746 is 2
Notice that 2 = HCF(6,2) = HCF(104,6) = HCF(110,104) = HCF(874,110) = HCF(984,874) = HCF(8746,984) .
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Frequently Asked Questions on HCF of 984, 8746 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, 8746?
Answer: HCF of 984, 8746 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 984, 8746 using Euclid's Algorithm?
Answer: For arbitrary numbers 984, 8746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.