Highest Common Factor of 900, 575, 998 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, 575, 998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 575, 998 is 1 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, 575, 998 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, 575, 998 is 1.
HCF(900, 575, 998) = 1
HCF of 900, 575, 998 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, 575, 998 is 1.
Highest Common Factor of 900,575,998 is 1
Step 1: Since 900 > 575, we apply the division lemma to 900 and 575, to get
900 = 575 x 1 + 325
Step 2: Since the reminder 575 ≠ 0, we apply division lemma to 325 and 575, to get
575 = 325 x 1 + 250
Step 3: We consider the new divisor 325 and the new remainder 250, and apply the division lemma to get
325 = 250 x 1 + 75
We consider the new divisor 250 and the new remainder 75,and apply the division lemma to get
250 = 75 x 3 + 25
We consider the new divisor 75 and the new remainder 25,and apply the division lemma to get
75 = 25 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 900 and 575 is 25
Notice that 25 = HCF(75,25) = HCF(250,75) = HCF(325,250) = HCF(575,325) = HCF(900,575) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 998 > 25, we apply the division lemma to 998 and 25, to get
998 = 25 x 39 + 23
Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 23 and 25, to get
25 = 23 x 1 + 2
Step 3: We consider the new divisor 23 and the new remainder 2, and apply the division lemma to get
23 = 2 x 11 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 25 and 998 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(998,25) .
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, 575, 998 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, 575, 998?
Answer: HCF of 900, 575, 998 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 575, 998 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 575, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
