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 2170, 1496, 30071 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2170, 1496, 30071 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 2170, 1496, 30071 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 2170, 1496, 30071 is 1.
HCF(2170, 1496, 30071) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2170, 1496, 30071 is 1.
Step 1: Since 2170 > 1496, we apply the division lemma to 2170 and 1496, to get
2170 = 1496 x 1 + 674
Step 2: Since the reminder 1496 ≠ 0, we apply division lemma to 674 and 1496, to get
1496 = 674 x 2 + 148
Step 3: We consider the new divisor 674 and the new remainder 148, and apply the division lemma to get
674 = 148 x 4 + 82
We consider the new divisor 148 and the new remainder 82,and apply the division lemma to get
148 = 82 x 1 + 66
We consider the new divisor 82 and the new remainder 66,and apply the division lemma to get
82 = 66 x 1 + 16
We consider the new divisor 66 and the new remainder 16,and apply the division lemma to get
66 = 16 x 4 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2170 and 1496 is 2
Notice that 2 = HCF(16,2) = HCF(66,16) = HCF(82,66) = HCF(148,82) = HCF(674,148) = HCF(1496,674) = HCF(2170,1496) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30071 > 2, we apply the division lemma to 30071 and 2, to get
30071 = 2 x 15035 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 30071 is 1
Notice that 1 = HCF(2,1) = HCF(30071,2) .
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 2170, 1496, 30071?
Answer: HCF of 2170, 1496, 30071 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2170, 1496, 30071 using Euclid's Algorithm?
Answer: For arbitrary numbers 2170, 1496, 30071 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.