Highest Common Factor of 682, 984 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 682, 984 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 984 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 682, 984 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 682, 984 is 2.
HCF(682, 984) = 2
HCF of 682, 984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 682, 984 is 2.
Highest Common Factor of 682,984 is 2
Step 1: Since 984 > 682, we apply the division lemma to 984 and 682, to get
984 = 682 x 1 + 302
Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 302 and 682, to get
682 = 302 x 2 + 78
Step 3: We consider the new divisor 302 and the new remainder 78, and apply the division lemma to get
302 = 78 x 3 + 68
We consider the new divisor 78 and the new remainder 68,and apply the division lemma to get
78 = 68 x 1 + 10
We consider the new divisor 68 and the new remainder 10,and apply the division lemma to get
68 = 10 x 6 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 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 682 and 984 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(68,10) = HCF(78,68) = HCF(302,78) = HCF(682,302) = HCF(984,682) .
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Frequently Asked Questions on HCF of 682, 984 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 682, 984?
Answer: HCF of 682, 984 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 984 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.