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, 935, 860 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 935, 860 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, 935, 860 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, 935, 860 is 1.
HCF(687, 935, 860) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 935, 860 is 1.
Step 1: Since 935 > 687, we apply the division lemma to 935 and 687, to get
935 = 687 x 1 + 248
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 248 and 687, to get
687 = 248 x 2 + 191
Step 3: We consider the new divisor 248 and the new remainder 191, and apply the division lemma to get
248 = 191 x 1 + 57
We consider the new divisor 191 and the new remainder 57,and apply the division lemma to get
191 = 57 x 3 + 20
We consider the new divisor 57 and the new remainder 20,and apply the division lemma to get
57 = 20 x 2 + 17
We consider the new divisor 20 and the new remainder 17,and apply the division lemma to get
20 = 17 x 1 + 3
We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get
17 = 3 x 5 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 687 and 935 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(20,17) = HCF(57,20) = HCF(191,57) = HCF(248,191) = HCF(687,248) = HCF(935,687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 860 > 1, we apply the division lemma to 860 and 1, to get
860 = 1 x 860 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 860 is 1
Notice that 1 = HCF(860,1) .
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, 935, 860?
Answer: HCF of 687, 935, 860 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 935, 860 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 935, 860 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.