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, 505 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 505 is 5 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, 505 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, 505 is 5.
HCF(900, 505) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 505 is 5.
Step 1: Since 900 > 505, we apply the division lemma to 900 and 505, to get
900 = 505 x 1 + 395
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 395 and 505, to get
505 = 395 x 1 + 110
Step 3: We consider the new divisor 395 and the new remainder 110, and apply the division lemma to get
395 = 110 x 3 + 65
We consider the new divisor 110 and the new remainder 65,and apply the division lemma to get
110 = 65 x 1 + 45
We consider the new divisor 65 and the new remainder 45,and apply the division lemma to get
65 = 45 x 1 + 20
We consider the new divisor 45 and the new remainder 20,and apply the division lemma to get
45 = 20 x 2 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 900 and 505 is 5
Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(65,45) = HCF(110,65) = HCF(395,110) = HCF(505,395) = HCF(900,505) .
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 900, 505?
Answer: HCF of 900, 505 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 505 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.