Highest Common Factor of 900, 162, 915 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 900, 162, 915 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 162, 915 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 900, 162, 915 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 900, 162, 915 is 3.
HCF(900, 162, 915) = 3
HCF of 900, 162, 915 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 162, 915 is 3.
Highest Common Factor of 900,162,915 is 3
Step 1: Since 900 > 162, we apply the division lemma to 900 and 162, to get
900 = 162 x 5 + 90
Step 2: Since the reminder 162 ≠ 0, we apply division lemma to 90 and 162, to get
162 = 90 x 1 + 72
Step 3: We consider the new divisor 90 and the new remainder 72, and apply the division lemma to get
90 = 72 x 1 + 18
We consider the new divisor 72 and the new remainder 18, and apply the division lemma to get
72 = 18 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 900 and 162 is 18
Notice that 18 = HCF(72,18) = HCF(90,72) = HCF(162,90) = HCF(900,162) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 915 > 18, we apply the division lemma to 915 and 18, to get
915 = 18 x 50 + 15
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 15 and 18, to get
18 = 15 x 1 + 3
Step 3: We consider the new divisor 15 and the new remainder 3, and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 18 and 915 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(915,18) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 900, 162, 915 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 900, 162, 915?
Answer: HCF of 900, 162, 915 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 162, 915 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 162, 915 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.