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 2071, 164 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2071, 164 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 2071, 164 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 2071, 164 is 1.
HCF(2071, 164) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2071, 164 is 1.
Step 1: Since 2071 > 164, we apply the division lemma to 2071 and 164, to get
2071 = 164 x 12 + 103
Step 2: Since the reminder 164 ≠ 0, we apply division lemma to 103 and 164, to get
164 = 103 x 1 + 61
Step 3: We consider the new divisor 103 and the new remainder 61, and apply the division lemma to get
103 = 61 x 1 + 42
We consider the new divisor 61 and the new remainder 42,and apply the division lemma to get
61 = 42 x 1 + 19
We consider the new divisor 42 and the new remainder 19,and apply the division lemma to get
42 = 19 x 2 + 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 2071 and 164 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(42,19) = HCF(61,42) = HCF(103,61) = HCF(164,103) = HCF(2071,164) .
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 2071, 164?
Answer: HCF of 2071, 164 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2071, 164 using Euclid's Algorithm?
Answer: For arbitrary numbers 2071, 164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.