Highest Common Factor of 301, 1374, 2097 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 301, 1374, 2097 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 301, 1374, 2097 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 301, 1374, 2097 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 301, 1374, 2097 is 1.
HCF(301, 1374, 2097) = 1
HCF of 301, 1374, 2097 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 301, 1374, 2097 is 1.
Highest Common Factor of 301,1374,2097 is 1
Step 1: Since 1374 > 301, we apply the division lemma to 1374 and 301, to get
1374 = 301 x 4 + 170
Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 170 and 301, to get
301 = 170 x 1 + 131
Step 3: We consider the new divisor 170 and the new remainder 131, and apply the division lemma to get
170 = 131 x 1 + 39
We consider the new divisor 131 and the new remainder 39,and apply the division lemma to get
131 = 39 x 3 + 14
We consider the new divisor 39 and the new remainder 14,and apply the division lemma to get
39 = 14 x 2 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 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 301 and 1374 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(39,14) = HCF(131,39) = HCF(170,131) = HCF(301,170) = HCF(1374,301) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2097 > 1, we apply the division lemma to 2097 and 1, to get
2097 = 1 x 2097 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2097 is 1
Notice that 1 = HCF(2097,1) .
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Frequently Asked Questions on HCF of 301, 1374, 2097 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 301, 1374, 2097?
Answer: HCF of 301, 1374, 2097 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 301, 1374, 2097 using Euclid's Algorithm?
Answer: For arbitrary numbers 301, 1374, 2097 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.