Highest Common Factor of 3124, 2294, 55111 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 3124, 2294, 55111 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3124, 2294, 55111 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 3124, 2294, 55111 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 3124, 2294, 55111 is 1.
HCF(3124, 2294, 55111) = 1
HCF of 3124, 2294, 55111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3124, 2294, 55111 is 1.
Highest Common Factor of 3124,2294,55111 is 1
Step 1: Since 3124 > 2294, we apply the division lemma to 3124 and 2294, to get
3124 = 2294 x 1 + 830
Step 2: Since the reminder 2294 ≠ 0, we apply division lemma to 830 and 2294, to get
2294 = 830 x 2 + 634
Step 3: We consider the new divisor 830 and the new remainder 634, and apply the division lemma to get
830 = 634 x 1 + 196
We consider the new divisor 634 and the new remainder 196,and apply the division lemma to get
634 = 196 x 3 + 46
We consider the new divisor 196 and the new remainder 46,and apply the division lemma to get
196 = 46 x 4 + 12
We consider the new divisor 46 and the new remainder 12,and apply the division lemma to get
46 = 12 x 3 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3124 and 2294 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(46,12) = HCF(196,46) = HCF(634,196) = HCF(830,634) = HCF(2294,830) = HCF(3124,2294) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55111 > 2, we apply the division lemma to 55111 and 2, to get
55111 = 2 x 27555 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 55111 is 1
Notice that 1 = HCF(2,1) = HCF(55111,2) .
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Frequently Asked Questions on HCF of 3124, 2294, 55111 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 3124, 2294, 55111?
Answer: HCF of 3124, 2294, 55111 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3124, 2294, 55111 using Euclid's Algorithm?
Answer: For arbitrary numbers 3124, 2294, 55111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.