Highest Common Factor of 656, 410, 305 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 656, 410, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 410, 305 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 656, 410, 305 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 656, 410, 305 is 1.
HCF(656, 410, 305) = 1
HCF of 656, 410, 305 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 410, 305 is 1.
Highest Common Factor of 656,410,305 is 1
Step 1: Since 656 > 410, we apply the division lemma to 656 and 410, to get
656 = 410 x 1 + 246
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 246 and 410, to get
410 = 246 x 1 + 164
Step 3: We consider the new divisor 246 and the new remainder 164, and apply the division lemma to get
246 = 164 x 1 + 82
We consider the new divisor 164 and the new remainder 82, and apply the division lemma to get
164 = 82 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 82, the HCF of 656 and 410 is 82
Notice that 82 = HCF(164,82) = HCF(246,164) = HCF(410,246) = HCF(656,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 305 > 82, we apply the division lemma to 305 and 82, to get
305 = 82 x 3 + 59
Step 2: Since the reminder 82 ≠ 0, we apply division lemma to 59 and 82, to get
82 = 59 x 1 + 23
Step 3: We consider the new divisor 59 and the new remainder 23, and apply the division lemma to get
59 = 23 x 2 + 13
We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 82 and 305 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(59,23) = HCF(82,59) = HCF(305,82) .
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Frequently Asked Questions on HCF of 656, 410, 305 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 656, 410, 305?
Answer: HCF of 656, 410, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 410, 305 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 410, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.