Highest Common Factor of 228, 999, 408, 88 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, 999, 408, 88 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 228, 999, 408, 88 is 1 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, 999, 408, 88 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, 999, 408, 88 is 1.
HCF(228, 999, 408, 88) = 1
HCF of 228, 999, 408, 88 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, 999, 408, 88 is 1.
Highest Common Factor of 228,999,408,88 is 1
Step 1: Since 999 > 228, we apply the division lemma to 999 and 228, to get
999 = 228 x 4 + 87
Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 87 and 228, to get
228 = 87 x 2 + 54
Step 3: We consider the new divisor 87 and the new remainder 54, and apply the division lemma to get
87 = 54 x 1 + 33
We consider the new divisor 54 and the new remainder 33,and apply the division lemma to get
54 = 33 x 1 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 228 and 999 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(54,33) = HCF(87,54) = HCF(228,87) = HCF(999,228) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 408 > 3, we apply the division lemma to 408 and 3, to get
408 = 3 x 136 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 408 is 3
Notice that 3 = HCF(408,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 88 > 3, we apply the division lemma to 88 and 3, to get
88 = 3 x 29 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 88 is 1
Notice that 1 = HCF(3,1) = HCF(88,3) .
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Frequently Asked Questions on HCF of 228, 999, 408, 88 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, 999, 408, 88?
Answer: HCF of 228, 999, 408, 88 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 228, 999, 408, 88 using Euclid's Algorithm?
Answer: For arbitrary numbers 228, 999, 408, 88 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.