Highest Common Factor of 415, 691 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 415, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 415, 691 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 415, 691 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 415, 691 is 1.
HCF(415, 691) = 1
HCF of 415, 691 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 415, 691 is 1.
Highest Common Factor of 415,691 is 1
Step 1: Since 691 > 415, we apply the division lemma to 691 and 415, to get
691 = 415 x 1 + 276
Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 276 and 415, to get
415 = 276 x 1 + 139
Step 3: We consider the new divisor 276 and the new remainder 139, and apply the division lemma to get
276 = 139 x 1 + 137
We consider the new divisor 139 and the new remainder 137,and apply the division lemma to get
139 = 137 x 1 + 2
We consider the new divisor 137 and the new remainder 2,and apply the division lemma to get
137 = 2 x 68 + 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 415 and 691 is 1
Notice that 1 = HCF(2,1) = HCF(137,2) = HCF(139,137) = HCF(276,139) = HCF(415,276) = HCF(691,415) .
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Frequently Asked Questions on HCF of 415, 691 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 415, 691?
Answer: HCF of 415, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 415, 691 using Euclid's Algorithm?
Answer: For arbitrary numbers 415, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.