Highest Common Factor of 228, 608, 84 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, 608, 84 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 228, 608, 84 is 4 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, 608, 84 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, 608, 84 is 4.
HCF(228, 608, 84) = 4
HCF of 228, 608, 84 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, 608, 84 is 4.
Highest Common Factor of 228,608,84 is 4
Step 1: Since 608 > 228, we apply the division lemma to 608 and 228, to get
608 = 228 x 2 + 152
Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 152 and 228, to get
228 = 152 x 1 + 76
Step 3: We consider the new divisor 152 and the new remainder 76, and apply the division lemma to get
152 = 76 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 76, the HCF of 228 and 608 is 76
Notice that 76 = HCF(152,76) = HCF(228,152) = HCF(608,228) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 84 > 76, we apply the division lemma to 84 and 76, to get
84 = 76 x 1 + 8
Step 2: Since the reminder 76 ≠ 0, we apply division lemma to 8 and 76, to get
76 = 8 x 9 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 76 and 84 is 4
Notice that 4 = HCF(8,4) = HCF(76,8) = HCF(84,76) .
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Frequently Asked Questions on HCF of 228, 608, 84 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, 608, 84?
Answer: HCF of 228, 608, 84 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 228, 608, 84 using Euclid's Algorithm?
Answer: For arbitrary numbers 228, 608, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.