Highest Common Factor of 996, 2145, 3187 using Euclid's algorithm
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, 2145, 3187 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 2145, 3187 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, 2145, 3187 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, 2145, 3187 is 1.
HCF(996, 2145, 3187) = 1
HCF of 996, 2145, 3187 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 996, 2145, 3187 is 1.
Highest Common Factor of 996,2145,3187 is 1
Step 1: Since 2145 > 996, we apply the division lemma to 2145 and 996, to get
2145 = 996 x 2 + 153
Step 2: Since the reminder 996 ≠ 0, we apply division lemma to 153 and 996, to get
996 = 153 x 6 + 78
Step 3: We consider the new divisor 153 and the new remainder 78, and apply the division lemma to get
153 = 78 x 1 + 75
We consider the new divisor 78 and the new remainder 75,and apply the division lemma to get
78 = 75 x 1 + 3
We consider the new divisor 75 and the new remainder 3,and apply the division lemma to get
75 = 3 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 996 and 2145 is 3
Notice that 3 = HCF(75,3) = HCF(78,75) = HCF(153,78) = HCF(996,153) = HCF(2145,996) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3187 > 3, we apply the division lemma to 3187 and 3, to get
3187 = 3 x 1062 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 3187 is 1
Notice that 1 = HCF(3,1) = HCF(3187,3) .
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Frequently Asked Questions on HCF of 996, 2145, 3187 using Euclid's Algorithm
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, 2145, 3187?
Answer: HCF of 996, 2145, 3187 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 2145, 3187 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 2145, 3187 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
