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 976, 687, 941 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 976, 687, 941 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 976, 687, 941 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 976, 687, 941 is 1.
HCF(976, 687, 941) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 976, 687, 941 is 1.
Step 1: Since 976 > 687, we apply the division lemma to 976 and 687, to get
976 = 687 x 1 + 289
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 289 and 687, to get
687 = 289 x 2 + 109
Step 3: We consider the new divisor 289 and the new remainder 109, and apply the division lemma to get
289 = 109 x 2 + 71
We consider the new divisor 109 and the new remainder 71,and apply the division lemma to get
109 = 71 x 1 + 38
We consider the new divisor 71 and the new remainder 38,and apply the division lemma to get
71 = 38 x 1 + 33
We consider the new divisor 38 and the new remainder 33,and apply the division lemma to get
38 = 33 x 1 + 5
We consider the new divisor 33 and the new remainder 5,and apply the division lemma to get
33 = 5 x 6 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 976 and 687 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(33,5) = HCF(38,33) = HCF(71,38) = HCF(109,71) = HCF(289,109) = HCF(687,289) = HCF(976,687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 941 > 1, we apply the division lemma to 941 and 1, to get
941 = 1 x 941 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 941 is 1
Notice that 1 = HCF(941,1) .
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 976, 687, 941?
Answer: HCF of 976, 687, 941 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 976, 687, 941 using Euclid's Algorithm?
Answer: For arbitrary numbers 976, 687, 941 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.