Highest Common Factor of 2910, 3406 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 2910, 3406 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2910, 3406 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 2910, 3406 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 2910, 3406 is 2.
HCF(2910, 3406) = 2
HCF of 2910, 3406 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2910, 3406 is 2.
Highest Common Factor of 2910,3406 is 2
Step 1: Since 3406 > 2910, we apply the division lemma to 3406 and 2910, to get
3406 = 2910 x 1 + 496
Step 2: Since the reminder 2910 ≠ 0, we apply division lemma to 496 and 2910, to get
2910 = 496 x 5 + 430
Step 3: We consider the new divisor 496 and the new remainder 430, and apply the division lemma to get
496 = 430 x 1 + 66
We consider the new divisor 430 and the new remainder 66,and apply the division lemma to get
430 = 66 x 6 + 34
We consider the new divisor 66 and the new remainder 34,and apply the division lemma to get
66 = 34 x 1 + 32
We consider the new divisor 34 and the new remainder 32,and apply the division lemma to get
34 = 32 x 1 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2910 and 3406 is 2
Notice that 2 = HCF(32,2) = HCF(34,32) = HCF(66,34) = HCF(430,66) = HCF(496,430) = HCF(2910,496) = HCF(3406,2910) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2910, 3406 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 2910, 3406?
Answer: HCF of 2910, 3406 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2910, 3406 using Euclid's Algorithm?
Answer: For arbitrary numbers 2910, 3406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.