Highest Common Factor of 888, 351, 135 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 888, 351, 135 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 888, 351, 135 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 888, 351, 135 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 888, 351, 135 is 3.
HCF(888, 351, 135) = 3
HCF of 888, 351, 135 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 888, 351, 135 is 3.
Highest Common Factor of 888,351,135 is 3
Step 1: Since 888 > 351, we apply the division lemma to 888 and 351, to get
888 = 351 x 2 + 186
Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 186 and 351, to get
351 = 186 x 1 + 165
Step 3: We consider the new divisor 186 and the new remainder 165, and apply the division lemma to get
186 = 165 x 1 + 21
We consider the new divisor 165 and the new remainder 21,and apply the division lemma to get
165 = 21 x 7 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 888 and 351 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(165,21) = HCF(186,165) = HCF(351,186) = HCF(888,351) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 135 > 3, we apply the division lemma to 135 and 3, to get
135 = 3 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 135 is 3
Notice that 3 = HCF(135,3) .
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Frequently Asked Questions on HCF of 888, 351, 135 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 888, 351, 135?
Answer: HCF of 888, 351, 135 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 888, 351, 135 using Euclid's Algorithm?
Answer: For arbitrary numbers 888, 351, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.