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 2106, 5342 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2106, 5342 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 2106, 5342 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 2106, 5342 is 2.
HCF(2106, 5342) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2106, 5342 is 2.
Step 1: Since 5342 > 2106, we apply the division lemma to 5342 and 2106, to get
5342 = 2106 x 2 + 1130
Step 2: Since the reminder 2106 ≠ 0, we apply division lemma to 1130 and 2106, to get
2106 = 1130 x 1 + 976
Step 3: We consider the new divisor 1130 and the new remainder 976, and apply the division lemma to get
1130 = 976 x 1 + 154
We consider the new divisor 976 and the new remainder 154,and apply the division lemma to get
976 = 154 x 6 + 52
We consider the new divisor 154 and the new remainder 52,and apply the division lemma to get
154 = 52 x 2 + 50
We consider the new divisor 52 and the new remainder 50,and apply the division lemma to get
52 = 50 x 1 + 2
We consider the new divisor 50 and the new remainder 2,and apply the division lemma to get
50 = 2 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2106 and 5342 is 2
Notice that 2 = HCF(50,2) = HCF(52,50) = HCF(154,52) = HCF(976,154) = HCF(1130,976) = HCF(2106,1130) = HCF(5342,2106) .
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 2106, 5342?
Answer: HCF of 2106, 5342 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2106, 5342 using Euclid's Algorithm?
Answer: For arbitrary numbers 2106, 5342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.