Highest Common Factor of 613, 846, 105 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 613, 846, 105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 613, 846, 105 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 613, 846, 105 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 613, 846, 105 is 1.
HCF(613, 846, 105) = 1
HCF of 613, 846, 105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 613, 846, 105 is 1.
Highest Common Factor of 613,846,105 is 1
Step 1: Since 846 > 613, we apply the division lemma to 846 and 613, to get
846 = 613 x 1 + 233
Step 2: Since the reminder 613 ≠ 0, we apply division lemma to 233 and 613, to get
613 = 233 x 2 + 147
Step 3: We consider the new divisor 233 and the new remainder 147, and apply the division lemma to get
233 = 147 x 1 + 86
We consider the new divisor 147 and the new remainder 86,and apply the division lemma to get
147 = 86 x 1 + 61
We consider the new divisor 86 and the new remainder 61,and apply the division lemma to get
86 = 61 x 1 + 25
We consider the new divisor 61 and the new remainder 25,and apply the division lemma to get
61 = 25 x 2 + 11
We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get
25 = 11 x 2 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 613 and 846 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(61,25) = HCF(86,61) = HCF(147,86) = HCF(233,147) = HCF(613,233) = HCF(846,613) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get
105 = 1 x 105 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1
Notice that 1 = HCF(105,1) .
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Frequently Asked Questions on HCF of 613, 846, 105 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 613, 846, 105?
Answer: HCF of 613, 846, 105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 613, 846, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 613, 846, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
