Highest Common Factor of 738, 471 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 738, 471 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 738, 471 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 738, 471 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 738, 471 is 3.
HCF(738, 471) = 3
HCF of 738, 471 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 738, 471 is 3.
Highest Common Factor of 738,471 is 3
Step 1: Since 738 > 471, we apply the division lemma to 738 and 471, to get
738 = 471 x 1 + 267
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 267 and 471, to get
471 = 267 x 1 + 204
Step 3: We consider the new divisor 267 and the new remainder 204, and apply the division lemma to get
267 = 204 x 1 + 63
We consider the new divisor 204 and the new remainder 63,and apply the division lemma to get
204 = 63 x 3 + 15
We consider the new divisor 63 and the new remainder 15,and apply the division lemma to get
63 = 15 x 4 + 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 738 and 471 is 3
Notice that 3 = HCF(15,3) = HCF(63,15) = HCF(204,63) = HCF(267,204) = HCF(471,267) = HCF(738,471) .
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Frequently Asked Questions on HCF of 738, 471 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 738, 471?
Answer: HCF of 738, 471 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 738, 471 using Euclid's Algorithm?
Answer: For arbitrary numbers 738, 471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.