Highest Common Factor of 504, 825 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 504, 825 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 825 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 504, 825 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 504, 825 is 3.
HCF(504, 825) = 3
HCF of 504, 825 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 825 is 3.
Highest Common Factor of 504,825 is 3
Step 1: Since 825 > 504, we apply the division lemma to 825 and 504, to get
825 = 504 x 1 + 321
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 321 and 504, to get
504 = 321 x 1 + 183
Step 3: We consider the new divisor 321 and the new remainder 183, and apply the division lemma to get
321 = 183 x 1 + 138
We consider the new divisor 183 and the new remainder 138,and apply the division lemma to get
183 = 138 x 1 + 45
We consider the new divisor 138 and the new remainder 45,and apply the division lemma to get
138 = 45 x 3 + 3
We consider the new divisor 45 and the new remainder 3,and apply the division lemma to get
45 = 3 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 504 and 825 is 3
Notice that 3 = HCF(45,3) = HCF(138,45) = HCF(183,138) = HCF(321,183) = HCF(504,321) = HCF(825,504) .
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Frequently Asked Questions on HCF of 504, 825 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 504, 825?
Answer: HCF of 504, 825 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 825 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 825 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.