Highest Common Factor of 1993, 1414 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 1993, 1414 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1993, 1414 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 1993, 1414 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 1993, 1414 is 1.
HCF(1993, 1414) = 1
HCF of 1993, 1414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1993, 1414 is 1.
Highest Common Factor of 1993,1414 is 1
Step 1: Since 1993 > 1414, we apply the division lemma to 1993 and 1414, to get
1993 = 1414 x 1 + 579
Step 2: Since the reminder 1414 ≠ 0, we apply division lemma to 579 and 1414, to get
1414 = 579 x 2 + 256
Step 3: We consider the new divisor 579 and the new remainder 256, and apply the division lemma to get
579 = 256 x 2 + 67
We consider the new divisor 256 and the new remainder 67,and apply the division lemma to get
256 = 67 x 3 + 55
We consider the new divisor 67 and the new remainder 55,and apply the division lemma to get
67 = 55 x 1 + 12
We consider the new divisor 55 and the new remainder 12,and apply the division lemma to get
55 = 12 x 4 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 1993 and 1414 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(55,12) = HCF(67,55) = HCF(256,67) = HCF(579,256) = HCF(1414,579) = HCF(1993,1414) .
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Frequently Asked Questions on HCF of 1993, 1414 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 1993, 1414?
Answer: HCF of 1993, 1414 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1993, 1414 using Euclid's Algorithm?
Answer: For arbitrary numbers 1993, 1414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.