Highest Common Factor of 198, 363, 705 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 198, 363, 705 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 198, 363, 705 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 198, 363, 705 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 198, 363, 705 is 3.
HCF(198, 363, 705) = 3
HCF of 198, 363, 705 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 198, 363, 705 is 3.
Highest Common Factor of 198,363,705 is 3
Step 1: Since 363 > 198, we apply the division lemma to 363 and 198, to get
363 = 198 x 1 + 165
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 165 and 198, to get
198 = 165 x 1 + 33
Step 3: We consider the new divisor 165 and the new remainder 33, and apply the division lemma to get
165 = 33 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 33, the HCF of 198 and 363 is 33
Notice that 33 = HCF(165,33) = HCF(198,165) = HCF(363,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 705 > 33, we apply the division lemma to 705 and 33, to get
705 = 33 x 21 + 12
Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 12 and 33, to get
33 = 12 x 2 + 9
Step 3: We consider the new divisor 12 and the new remainder 9, and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 33 and 705 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(705,33) .
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Frequently Asked Questions on HCF of 198, 363, 705 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 198, 363, 705?
Answer: HCF of 198, 363, 705 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 198, 363, 705 using Euclid's Algorithm?
Answer: For arbitrary numbers 198, 363, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.