Highest Common Factor of 604, 234, 284 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 604, 234, 284 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 604, 234, 284 is 2 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 604, 234, 284 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 604, 234, 284 is 2.
HCF(604, 234, 284) = 2
HCF of 604, 234, 284 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 604, 234, 284 is 2.
Highest Common Factor of 604,234,284 is 2
Step 1: Since 604 > 234, we apply the division lemma to 604 and 234, to get
604 = 234 x 2 + 136
Step 2: Since the reminder 234 ≠ 0, we apply division lemma to 136 and 234, to get
234 = 136 x 1 + 98
Step 3: We consider the new divisor 136 and the new remainder 98, and apply the division lemma to get
136 = 98 x 1 + 38
We consider the new divisor 98 and the new remainder 38,and apply the division lemma to get
98 = 38 x 2 + 22
We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get
38 = 22 x 1 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 604 and 234 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(98,38) = HCF(136,98) = HCF(234,136) = HCF(604,234) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 284 > 2, we apply the division lemma to 284 and 2, to get
284 = 2 x 142 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 284 is 2
Notice that 2 = HCF(284,2) .
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Frequently Asked Questions on HCF of 604, 234, 284 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 604, 234, 284?
Answer: HCF of 604, 234, 284 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 604, 234, 284 using Euclid's Algorithm?
Answer: For arbitrary numbers 604, 234, 284 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.