Highest Common Factor of 436, 304, 474 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 436, 304, 474 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 436, 304, 474 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 436, 304, 474 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 436, 304, 474 is 2.
HCF(436, 304, 474) = 2
HCF of 436, 304, 474 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 436, 304, 474 is 2.
Highest Common Factor of 436,304,474 is 2
Step 1: Since 436 > 304, we apply the division lemma to 436 and 304, to get
436 = 304 x 1 + 132
Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 132 and 304, to get
304 = 132 x 2 + 40
Step 3: We consider the new divisor 132 and the new remainder 40, and apply the division lemma to get
132 = 40 x 3 + 12
We consider the new divisor 40 and the new remainder 12,and apply the division lemma to get
40 = 12 x 3 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 436 and 304 is 4
Notice that 4 = HCF(12,4) = HCF(40,12) = HCF(132,40) = HCF(304,132) = HCF(436,304) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 474 > 4, we apply the division lemma to 474 and 4, to get
474 = 4 x 118 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 474 is 2
Notice that 2 = HCF(4,2) = HCF(474,4) .
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Frequently Asked Questions on HCF of 436, 304, 474 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 436, 304, 474?
Answer: HCF of 436, 304, 474 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 436, 304, 474 using Euclid's Algorithm?
Answer: For arbitrary numbers 436, 304, 474 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.