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 687, 9340 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 9340 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 687, 9340 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 687, 9340 is 1.
HCF(687, 9340) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 9340 is 1.
Step 1: Since 9340 > 687, we apply the division lemma to 9340 and 687, to get
9340 = 687 x 13 + 409
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 409 and 687, to get
687 = 409 x 1 + 278
Step 3: We consider the new divisor 409 and the new remainder 278, and apply the division lemma to get
409 = 278 x 1 + 131
We consider the new divisor 278 and the new remainder 131,and apply the division lemma to get
278 = 131 x 2 + 16
We consider the new divisor 131 and the new remainder 16,and apply the division lemma to get
131 = 16 x 8 + 3
We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get
16 = 3 x 5 + 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 687 and 9340 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(131,16) = HCF(278,131) = HCF(409,278) = HCF(687,409) = HCF(9340,687) .
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 687, 9340?
Answer: HCF of 687, 9340 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 9340 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 9340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.