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 2151, 6228 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 2151, 6228 is 9 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 2151, 6228 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 2151, 6228 is 9.
HCF(2151, 6228) = 9
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2151, 6228 is 9.
Step 1: Since 6228 > 2151, we apply the division lemma to 6228 and 2151, to get
6228 = 2151 x 2 + 1926
Step 2: Since the reminder 2151 ≠ 0, we apply division lemma to 1926 and 2151, to get
2151 = 1926 x 1 + 225
Step 3: We consider the new divisor 1926 and the new remainder 225, and apply the division lemma to get
1926 = 225 x 8 + 126
We consider the new divisor 225 and the new remainder 126,and apply the division lemma to get
225 = 126 x 1 + 99
We consider the new divisor 126 and the new remainder 99,and apply the division lemma to get
126 = 99 x 1 + 27
We consider the new divisor 99 and the new remainder 27,and apply the division lemma to get
99 = 27 x 3 + 18
We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 2151 and 6228 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(99,27) = HCF(126,99) = HCF(225,126) = HCF(1926,225) = HCF(2151,1926) = HCF(6228,2151) .
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 2151, 6228?
Answer: HCF of 2151, 6228 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2151, 6228 using Euclid's Algorithm?
Answer: For arbitrary numbers 2151, 6228 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.