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 1682, 9688 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1682, 9688 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 1682, 9688 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 1682, 9688 is 2.
HCF(1682, 9688) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1682, 9688 is 2.
Step 1: Since 9688 > 1682, we apply the division lemma to 9688 and 1682, to get
9688 = 1682 x 5 + 1278
Step 2: Since the reminder 1682 ≠ 0, we apply division lemma to 1278 and 1682, to get
1682 = 1278 x 1 + 404
Step 3: We consider the new divisor 1278 and the new remainder 404, and apply the division lemma to get
1278 = 404 x 3 + 66
We consider the new divisor 404 and the new remainder 66,and apply the division lemma to get
404 = 66 x 6 + 8
We consider the new divisor 66 and the new remainder 8,and apply the division lemma to get
66 = 8 x 8 + 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 1682 and 9688 is 2
Notice that 2 = HCF(8,2) = HCF(66,8) = HCF(404,66) = HCF(1278,404) = HCF(1682,1278) = HCF(9688,1682) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 1682, 9688?
Answer: HCF of 1682, 9688 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1682, 9688 using Euclid's Algorithm?
Answer: For arbitrary numbers 1682, 9688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.