Highest Common Factor of 982, 144 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 982, 144 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 982, 144 is 2 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 982, 144 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 982, 144 is 2.
HCF(982, 144) = 2
HCF of 982, 144 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 982, 144 is 2.
Highest Common Factor of 982,144 is 2
Step 1: Since 982 > 144, we apply the division lemma to 982 and 144, to get
982 = 144 x 6 + 118
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 118 and 144, to get
144 = 118 x 1 + 26
Step 3: We consider the new divisor 118 and the new remainder 26, and apply the division lemma to get
118 = 26 x 4 + 14
We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 982 and 144 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(118,26) = HCF(144,118) = HCF(982,144) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 982, 144 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 982, 144?
Answer: HCF of 982, 144 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 982, 144 using Euclid's Algorithm?
Answer: For arbitrary numbers 982, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.