Highest Common Factor of 228, 2175, 3561 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 228, 2175, 3561 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 228, 2175, 3561 is 3 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 228, 2175, 3561 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 228, 2175, 3561 is 3.
HCF(228, 2175, 3561) = 3
HCF of 228, 2175, 3561 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 228, 2175, 3561 is 3.
Highest Common Factor of 228,2175,3561 is 3
Step 1: Since 2175 > 228, we apply the division lemma to 2175 and 228, to get
2175 = 228 x 9 + 123
Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 123 and 228, to get
228 = 123 x 1 + 105
Step 3: We consider the new divisor 123 and the new remainder 105, and apply the division lemma to get
123 = 105 x 1 + 18
We consider the new divisor 105 and the new remainder 18,and apply the division lemma to get
105 = 18 x 5 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 228 and 2175 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(105,18) = HCF(123,105) = HCF(228,123) = HCF(2175,228) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3561 > 3, we apply the division lemma to 3561 and 3, to get
3561 = 3 x 1187 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 3561 is 3
Notice that 3 = HCF(3561,3) .
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Frequently Asked Questions on HCF of 228, 2175, 3561 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 228, 2175, 3561?
Answer: HCF of 228, 2175, 3561 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 228, 2175, 3561 using Euclid's Algorithm?
Answer: For arbitrary numbers 228, 2175, 3561 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.