Highest Common Factor of 705, 198, 285 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 705, 198, 285 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 198, 285 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 705, 198, 285 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 705, 198, 285 is 3.
HCF(705, 198, 285) = 3
HCF of 705, 198, 285 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 198, 285 is 3.
Highest Common Factor of 705,198,285 is 3
Step 1: Since 705 > 198, we apply the division lemma to 705 and 198, to get
705 = 198 x 3 + 111
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 111 and 198, to get
198 = 111 x 1 + 87
Step 3: We consider the new divisor 111 and the new remainder 87, and apply the division lemma to get
111 = 87 x 1 + 24
We consider the new divisor 87 and the new remainder 24,and apply the division lemma to get
87 = 24 x 3 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 705 and 198 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(87,24) = HCF(111,87) = HCF(198,111) = HCF(705,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 285 > 3, we apply the division lemma to 285 and 3, to get
285 = 3 x 95 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 285 is 3
Notice that 3 = HCF(285,3) .
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Frequently Asked Questions on HCF of 705, 198, 285 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 705, 198, 285?
Answer: HCF of 705, 198, 285 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 198, 285 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 198, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.