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 1902, 8124 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 1902, 8124 is 6 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 1902, 8124 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 1902, 8124 is 6.
HCF(1902, 8124) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1902, 8124 is 6.
Step 1: Since 8124 > 1902, we apply the division lemma to 8124 and 1902, to get
8124 = 1902 x 4 + 516
Step 2: Since the reminder 1902 ≠ 0, we apply division lemma to 516 and 1902, to get
1902 = 516 x 3 + 354
Step 3: We consider the new divisor 516 and the new remainder 354, and apply the division lemma to get
516 = 354 x 1 + 162
We consider the new divisor 354 and the new remainder 162,and apply the division lemma to get
354 = 162 x 2 + 30
We consider the new divisor 162 and the new remainder 30,and apply the division lemma to get
162 = 30 x 5 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1902 and 8124 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(162,30) = HCF(354,162) = HCF(516,354) = HCF(1902,516) = HCF(8124,1902) .
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 1902, 8124?
Answer: HCF of 1902, 8124 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1902, 8124 using Euclid's Algorithm?
Answer: For arbitrary numbers 1902, 8124 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.