Highest Common Factor of 150, 200, 180 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 150, 200, 180 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 150, 200, 180 is 10 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 150, 200, 180 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 150, 200, 180 is 10.
HCF(150, 200, 180) = 10
HCF of 150, 200, 180 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 150, 200, 180 is 10.
Highest Common Factor of 150,200,180 is 10
Step 1: Since 200 > 150, we apply the division lemma to 200 and 150, to get
200 = 150 x 1 + 50
Step 2: Since the reminder 150 ≠ 0, we apply division lemma to 50 and 150, to get
150 = 50 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 50, the HCF of 150 and 200 is 50
Notice that 50 = HCF(150,50) = HCF(200,150) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 180 > 50, we apply the division lemma to 180 and 50, to get
180 = 50 x 3 + 30
Step 2: Since the reminder 50 ≠ 0, we apply division lemma to 30 and 50, to get
50 = 30 x 1 + 20
Step 3: We consider the new divisor 30 and the new remainder 20, and apply the division lemma to get
30 = 20 x 1 + 10
We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 50 and 180 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(50,30) = HCF(180,50) .
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Frequently Asked Questions on HCF of 150, 200, 180 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 150, 200, 180?
Answer: HCF of 150, 200, 180 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 150, 200, 180 using Euclid's Algorithm?
Answer: For arbitrary numbers 150, 200, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.