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 867, 9314, 7319 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 867, 9314, 7319 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 867, 9314, 7319 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 867, 9314, 7319 is 1.
HCF(867, 9314, 7319) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 867, 9314, 7319 is 1.
Step 1: Since 9314 > 867, we apply the division lemma to 9314 and 867, to get
9314 = 867 x 10 + 644
Step 2: Since the reminder 867 ≠ 0, we apply division lemma to 644 and 867, to get
867 = 644 x 1 + 223
Step 3: We consider the new divisor 644 and the new remainder 223, and apply the division lemma to get
644 = 223 x 2 + 198
We consider the new divisor 223 and the new remainder 198,and apply the division lemma to get
223 = 198 x 1 + 25
We consider the new divisor 198 and the new remainder 25,and apply the division lemma to get
198 = 25 x 7 + 23
We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get
25 = 23 x 1 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 867 and 9314 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(198,25) = HCF(223,198) = HCF(644,223) = HCF(867,644) = HCF(9314,867) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7319 > 1, we apply the division lemma to 7319 and 1, to get
7319 = 1 x 7319 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7319 is 1
Notice that 1 = HCF(7319,1) .
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 867, 9314, 7319?
Answer: HCF of 867, 9314, 7319 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 867, 9314, 7319 using Euclid's Algorithm?
Answer: For arbitrary numbers 867, 9314, 7319 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.