Highest Common Factor of 1982, 523 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 1982, 523 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1982, 523 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 1982, 523 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 1982, 523 is 1.
HCF(1982, 523) = 1
HCF of 1982, 523 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1982, 523 is 1.
Highest Common Factor of 1982,523 is 1
Step 1: Since 1982 > 523, we apply the division lemma to 1982 and 523, to get
1982 = 523 x 3 + 413
Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 413 and 523, to get
523 = 413 x 1 + 110
Step 3: We consider the new divisor 413 and the new remainder 110, and apply the division lemma to get
413 = 110 x 3 + 83
We consider the new divisor 110 and the new remainder 83,and apply the division lemma to get
110 = 83 x 1 + 27
We consider the new divisor 83 and the new remainder 27,and apply the division lemma to get
83 = 27 x 3 + 2
We consider the new divisor 27 and the new remainder 2,and apply the division lemma to get
27 = 2 x 13 + 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 1982 and 523 is 1
Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(83,27) = HCF(110,83) = HCF(413,110) = HCF(523,413) = HCF(1982,523) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1982, 523 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 1982, 523?
Answer: HCF of 1982, 523 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1982, 523 using Euclid's Algorithm?
Answer: For arbitrary numbers 1982, 523 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.