Highest Common Factor of 1612, 2185, 97800 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 1612, 2185, 97800 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1612, 2185, 97800 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 1612, 2185, 97800 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 1612, 2185, 97800 is 1.
HCF(1612, 2185, 97800) = 1
HCF of 1612, 2185, 97800 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1612, 2185, 97800 is 1.
Highest Common Factor of 1612,2185,97800 is 1
Step 1: Since 2185 > 1612, we apply the division lemma to 2185 and 1612, to get
2185 = 1612 x 1 + 573
Step 2: Since the reminder 1612 ≠ 0, we apply division lemma to 573 and 1612, to get
1612 = 573 x 2 + 466
Step 3: We consider the new divisor 573 and the new remainder 466, and apply the division lemma to get
573 = 466 x 1 + 107
We consider the new divisor 466 and the new remainder 107,and apply the division lemma to get
466 = 107 x 4 + 38
We consider the new divisor 107 and the new remainder 38,and apply the division lemma to get
107 = 38 x 2 + 31
We consider the new divisor 38 and the new remainder 31,and apply the division lemma to get
38 = 31 x 1 + 7
We consider the new divisor 31 and the new remainder 7,and apply the division lemma to get
31 = 7 x 4 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 1612 and 2185 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(31,7) = HCF(38,31) = HCF(107,38) = HCF(466,107) = HCF(573,466) = HCF(1612,573) = HCF(2185,1612) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 97800 > 1, we apply the division lemma to 97800 and 1, to get
97800 = 1 x 97800 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 97800 is 1
Notice that 1 = HCF(97800,1) .
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Frequently Asked Questions on HCF of 1612, 2185, 97800 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 1612, 2185, 97800?
Answer: HCF of 1612, 2185, 97800 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1612, 2185, 97800 using Euclid's Algorithm?
Answer: For arbitrary numbers 1612, 2185, 97800 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
