Highest Common Factor of 3790, 4006, 30170 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 3790, 4006, 30170 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3790, 4006, 30170 is 2 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 3790, 4006, 30170 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 3790, 4006, 30170 is 2.
HCF(3790, 4006, 30170) = 2
HCF of 3790, 4006, 30170 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3790, 4006, 30170 is 2.
Highest Common Factor of 3790,4006,30170 is 2
Step 1: Since 4006 > 3790, we apply the division lemma to 4006 and 3790, to get
4006 = 3790 x 1 + 216
Step 2: Since the reminder 3790 ≠ 0, we apply division lemma to 216 and 3790, to get
3790 = 216 x 17 + 118
Step 3: We consider the new divisor 216 and the new remainder 118, and apply the division lemma to get
216 = 118 x 1 + 98
We consider the new divisor 118 and the new remainder 98,and apply the division lemma to get
118 = 98 x 1 + 20
We consider the new divisor 98 and the new remainder 20,and apply the division lemma to get
98 = 20 x 4 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3790 and 4006 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(98,20) = HCF(118,98) = HCF(216,118) = HCF(3790,216) = HCF(4006,3790) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30170 > 2, we apply the division lemma to 30170 and 2, to get
30170 = 2 x 15085 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 30170 is 2
Notice that 2 = HCF(30170,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3790, 4006, 30170 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 3790, 4006, 30170?
Answer: HCF of 3790, 4006, 30170 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3790, 4006, 30170 using Euclid's Algorithm?
Answer: For arbitrary numbers 3790, 4006, 30170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
