Highest Common Factor of 825, 300, 190 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, 300, 190 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 300, 190 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, 300, 190 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, 300, 190 is 5.
HCF(825, 300, 190) = 5
HCF of 825, 300, 190 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, 300, 190 is 5.
Highest Common Factor of 825,300,190 is 5
Step 1: Since 825 > 300, we apply the division lemma to 825 and 300, to get
825 = 300 x 2 + 225
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 225 and 300, to get
300 = 225 x 1 + 75
Step 3: We consider the new divisor 225 and the new remainder 75, and apply the division lemma to get
225 = 75 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 75, the HCF of 825 and 300 is 75
Notice that 75 = HCF(225,75) = HCF(300,225) = HCF(825,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 190 > 75, we apply the division lemma to 190 and 75, to get
190 = 75 x 2 + 40
Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 40 and 75, to get
75 = 40 x 1 + 35
Step 3: We consider the new divisor 40 and the new remainder 35, and apply the division lemma to get
40 = 35 x 1 + 5
We consider the new divisor 35 and the new remainder 5, and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 75 and 190 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(75,40) = HCF(190,75) .
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Frequently Asked Questions on HCF of 825, 300, 190 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, 300, 190?
Answer: HCF of 825, 300, 190 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 300, 190 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 300, 190 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.