Highest Common Factor of 825, 675, 450 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 825, 675, 450 i.e. 75 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 675, 450 is 75 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 825, 675, 450 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 825, 675, 450 is 75.
HCF(825, 675, 450) = 75
HCF of 825, 675, 450 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 825, 675, 450 is 75.
Highest Common Factor of 825,675,450 is 75
Step 1: Since 825 > 675, we apply the division lemma to 825 and 675, to get
825 = 675 x 1 + 150
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 150 and 675, to get
675 = 150 x 4 + 75
Step 3: We consider the new divisor 150 and the new remainder 75, and apply the division lemma to get
150 = 75 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 75, the HCF of 825 and 675 is 75
Notice that 75 = HCF(150,75) = HCF(675,150) = HCF(825,675) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 450 > 75, we apply the division lemma to 450 and 75, to get
450 = 75 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 75, the HCF of 75 and 450 is 75
Notice that 75 = HCF(450,75) .
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Frequently Asked Questions on HCF of 825, 675, 450 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 825, 675, 450?
Answer: HCF of 825, 675, 450 is 75 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 675, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 675, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.