Highest Common Factor of 825, 965, 200 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, 965, 200 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 965, 200 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 825, 965, 200 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, 965, 200 is 5.
HCF(825, 965, 200) = 5
HCF of 825, 965, 200 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, 965, 200 is 5.
Highest Common Factor of 825,965,200 is 5
Step 1: Since 965 > 825, we apply the division lemma to 965 and 825, to get
965 = 825 x 1 + 140
Step 2: Since the reminder 825 ≠ 0, we apply division lemma to 140 and 825, to get
825 = 140 x 5 + 125
Step 3: We consider the new divisor 140 and the new remainder 125, and apply the division lemma to get
140 = 125 x 1 + 15
We consider the new divisor 125 and the new remainder 15,and apply the division lemma to get
125 = 15 x 8 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 825 and 965 is 5
Notice that 5 = HCF(15,5) = HCF(125,15) = HCF(140,125) = HCF(825,140) = HCF(965,825) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 200 > 5, we apply the division lemma to 200 and 5, to get
200 = 5 x 40 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 200 is 5
Notice that 5 = HCF(200,5) .
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Frequently Asked Questions on HCF of 825, 965, 200 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, 965, 200?
Answer: HCF of 825, 965, 200 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 965, 200 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 965, 200 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.