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 2985, 189 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2985, 189 is 3 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 2985, 189 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 2985, 189 is 3.
HCF(2985, 189) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2985, 189 is 3.
Step 1: Since 2985 > 189, we apply the division lemma to 2985 and 189, to get
2985 = 189 x 15 + 150
Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 150 and 189, to get
189 = 150 x 1 + 39
Step 3: We consider the new divisor 150 and the new remainder 39, and apply the division lemma to get
150 = 39 x 3 + 33
We consider the new divisor 39 and the new remainder 33,and apply the division lemma to get
39 = 33 x 1 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2985 and 189 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(150,39) = HCF(189,150) = HCF(2985,189) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 2985, 189?
Answer: HCF of 2985, 189 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2985, 189 using Euclid's Algorithm?
Answer: For arbitrary numbers 2985, 189 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.