Highest Common Factor of 461, 1715 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 461, 1715 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 461, 1715 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 461, 1715 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 461, 1715 is 1.
HCF(461, 1715) = 1
HCF of 461, 1715 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 461, 1715 is 1.
Highest Common Factor of 461,1715 is 1
Step 1: Since 1715 > 461, we apply the division lemma to 1715 and 461, to get
1715 = 461 x 3 + 332
Step 2: Since the reminder 461 ≠ 0, we apply division lemma to 332 and 461, to get
461 = 332 x 1 + 129
Step 3: We consider the new divisor 332 and the new remainder 129, and apply the division lemma to get
332 = 129 x 2 + 74
We consider the new divisor 129 and the new remainder 74,and apply the division lemma to get
129 = 74 x 1 + 55
We consider the new divisor 74 and the new remainder 55,and apply the division lemma to get
74 = 55 x 1 + 19
We consider the new divisor 55 and the new remainder 19,and apply the division lemma to get
55 = 19 x 2 + 17
We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get
19 = 17 x 1 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 461 and 1715 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(55,19) = HCF(74,55) = HCF(129,74) = HCF(332,129) = HCF(461,332) = HCF(1715,461) .
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Frequently Asked Questions on HCF of 461, 1715 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 461, 1715?
Answer: HCF of 461, 1715 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 461, 1715 using Euclid's Algorithm?
Answer: For arbitrary numbers 461, 1715 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.