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 208, 3102 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 208, 3102 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 208, 3102 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 208, 3102 is 2.
HCF(208, 3102) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 208, 3102 is 2.
Step 1: Since 3102 > 208, we apply the division lemma to 3102 and 208, to get
3102 = 208 x 14 + 190
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 190 and 208, to get
208 = 190 x 1 + 18
Step 3: We consider the new divisor 190 and the new remainder 18, and apply the division lemma to get
190 = 18 x 10 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 208 and 3102 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(190,18) = HCF(208,190) = HCF(3102,208) .
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 208, 3102?
Answer: HCF of 208, 3102 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 208, 3102 using Euclid's Algorithm?
Answer: For arbitrary numbers 208, 3102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.