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 865, 976, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 865, 976, 40 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 865, 976, 40 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 865, 976, 40 is 1.
HCF(865, 976, 40) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 865, 976, 40 is 1.
Step 1: Since 976 > 865, we apply the division lemma to 976 and 865, to get
976 = 865 x 1 + 111
Step 2: Since the reminder 865 ≠ 0, we apply division lemma to 111 and 865, to get
865 = 111 x 7 + 88
Step 3: We consider the new divisor 111 and the new remainder 88, and apply the division lemma to get
111 = 88 x 1 + 23
We consider the new divisor 88 and the new remainder 23,and apply the division lemma to get
88 = 23 x 3 + 19
We consider the new divisor 23 and the new remainder 19,and apply the division lemma to get
23 = 19 x 1 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 865 and 976 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(23,19) = HCF(88,23) = HCF(111,88) = HCF(865,111) = HCF(976,865) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 40 > 1, we apply the division lemma to 40 and 1, to get
40 = 1 x 40 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 40 is 1
Notice that 1 = HCF(40,1) .
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 865, 976, 40?
Answer: HCF of 865, 976, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 865, 976, 40 using Euclid's Algorithm?
Answer: For arbitrary numbers 865, 976, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.