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 996, 277, 814 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 277, 814 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 996, 277, 814 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 996, 277, 814 is 1.
HCF(996, 277, 814) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 996, 277, 814 is 1.
Step 1: Since 996 > 277, we apply the division lemma to 996 and 277, to get
996 = 277 x 3 + 165
Step 2: Since the reminder 277 ≠ 0, we apply division lemma to 165 and 277, to get
277 = 165 x 1 + 112
Step 3: We consider the new divisor 165 and the new remainder 112, and apply the division lemma to get
165 = 112 x 1 + 53
We consider the new divisor 112 and the new remainder 53,and apply the division lemma to get
112 = 53 x 2 + 6
We consider the new divisor 53 and the new remainder 6,and apply the division lemma to get
53 = 6 x 8 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 996 and 277 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(53,6) = HCF(112,53) = HCF(165,112) = HCF(277,165) = HCF(996,277) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 1, we apply the division lemma to 814 and 1, to get
814 = 1 x 814 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 814 is 1
Notice that 1 = HCF(814,1) .
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 996, 277, 814?
Answer: HCF of 996, 277, 814 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 277, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 277, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.