Highest Common Factor of 471, 312, 751 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 471, 312, 751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 471, 312, 751 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 471, 312, 751 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 471, 312, 751 is 1.
HCF(471, 312, 751) = 1
HCF of 471, 312, 751 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 471, 312, 751 is 1.
Highest Common Factor of 471,312,751 is 1
Step 1: Since 471 > 312, we apply the division lemma to 471 and 312, to get
471 = 312 x 1 + 159
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 159 and 312, to get
312 = 159 x 1 + 153
Step 3: We consider the new divisor 159 and the new remainder 153, and apply the division lemma to get
159 = 153 x 1 + 6
We consider the new divisor 153 and the new remainder 6,and apply the division lemma to get
153 = 6 x 25 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 471 and 312 is 3
Notice that 3 = HCF(6,3) = HCF(153,6) = HCF(159,153) = HCF(312,159) = HCF(471,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 751 > 3, we apply the division lemma to 751 and 3, to get
751 = 3 x 250 + 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 751 is 1
Notice that 1 = HCF(3,1) = HCF(751,3) .
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Frequently Asked Questions on HCF of 471, 312, 751 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 471, 312, 751?
Answer: HCF of 471, 312, 751 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 471, 312, 751 using Euclid's Algorithm?
Answer: For arbitrary numbers 471, 312, 751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.