Highest Common Factor of 825, 648, 803 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, 648, 803 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 648, 803 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 825, 648, 803 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, 648, 803 is 1.
HCF(825, 648, 803) = 1
HCF of 825, 648, 803 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, 648, 803 is 1.
Highest Common Factor of 825,648,803 is 1
Step 1: Since 825 > 648, we apply the division lemma to 825 and 648, to get
825 = 648 x 1 + 177
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 177 and 648, to get
648 = 177 x 3 + 117
Step 3: We consider the new divisor 177 and the new remainder 117, and apply the division lemma to get
177 = 117 x 1 + 60
We consider the new divisor 117 and the new remainder 60,and apply the division lemma to get
117 = 60 x 1 + 57
We consider the new divisor 60 and the new remainder 57,and apply the division lemma to get
60 = 57 x 1 + 3
We consider the new divisor 57 and the new remainder 3,and apply the division lemma to get
57 = 3 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 825 and 648 is 3
Notice that 3 = HCF(57,3) = HCF(60,57) = HCF(117,60) = HCF(177,117) = HCF(648,177) = HCF(825,648) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 803 > 3, we apply the division lemma to 803 and 3, to get
803 = 3 x 267 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 803 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(803,3) .
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Frequently Asked Questions on HCF of 825, 648, 803 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, 648, 803?
Answer: HCF of 825, 648, 803 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 648, 803 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 648, 803 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
