Highest Common Factor of 1998, 2133 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 1998, 2133 i.e. 27 the largest integer that leaves a remainder zero for all numbers.
HCF of 1998, 2133 is 27 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 1998, 2133 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 1998, 2133 is 27.
HCF(1998, 2133) = 27
HCF of 1998, 2133 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1998, 2133 is 27.
Highest Common Factor of 1998,2133 is 27
Step 1: Since 2133 > 1998, we apply the division lemma to 2133 and 1998, to get
2133 = 1998 x 1 + 135
Step 2: Since the reminder 1998 ≠ 0, we apply division lemma to 135 and 1998, to get
1998 = 135 x 14 + 108
Step 3: We consider the new divisor 135 and the new remainder 108, and apply the division lemma to get
135 = 108 x 1 + 27
We consider the new divisor 108 and the new remainder 27, and apply the division lemma to get
108 = 27 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 1998 and 2133 is 27
Notice that 27 = HCF(108,27) = HCF(135,108) = HCF(1998,135) = HCF(2133,1998) .
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Frequently Asked Questions on HCF of 1998, 2133 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 1998, 2133?
Answer: HCF of 1998, 2133 is 27 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1998, 2133 using Euclid's Algorithm?
Answer: For arbitrary numbers 1998, 2133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
