Highest Common Factor of 257, 916, 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 257, 916, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 257, 916, 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 257, 916, 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 257, 916, 691 is 1.
HCF(257, 916, 691) = 1
HCF of 257, 916, 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 257, 916, 691 is 1.
Highest Common Factor of 257,916,691 is 1
Step 1: Since 916 > 257, we apply the division lemma to 916 and 257, to get
916 = 257 x 3 + 145
Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 145 and 257, to get
257 = 145 x 1 + 112
Step 3: We consider the new divisor 145 and the new remainder 112, and apply the division lemma to get
145 = 112 x 1 + 33
We consider the new divisor 112 and the new remainder 33,and apply the division lemma to get
112 = 33 x 3 + 13
We consider the new divisor 33 and the new remainder 13,and apply the division lemma to get
33 = 13 x 2 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 257 and 916 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(33,13) = HCF(112,33) = HCF(145,112) = HCF(257,145) = HCF(916,257) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 691 > 1, we apply the division lemma to 691 and 1, to get
691 = 1 x 691 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 691 is 1
Notice that 1 = HCF(691,1) .
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Frequently Asked Questions on HCF of 257, 916, 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 257, 916, 691?
Answer: HCF of 257, 916, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 257, 916, 691 using Euclid's Algorithm?
Answer: For arbitrary numbers 257, 916, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
