Highest Common Factor of 888, 342, 720 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, 342, 720 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 888, 342, 720 is 6 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, 342, 720 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, 342, 720 is 6.
HCF(888, 342, 720) = 6
HCF of 888, 342, 720 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, 342, 720 is 6.
Highest Common Factor of 888,342,720 is 6
Step 1: Since 888 > 342, we apply the division lemma to 888 and 342, to get
888 = 342 x 2 + 204
Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 204 and 342, to get
342 = 204 x 1 + 138
Step 3: We consider the new divisor 204 and the new remainder 138, and apply the division lemma to get
204 = 138 x 1 + 66
We consider the new divisor 138 and the new remainder 66,and apply the division lemma to get
138 = 66 x 2 + 6
We consider the new divisor 66 and the new remainder 6,and apply the division lemma to get
66 = 6 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 888 and 342 is 6
Notice that 6 = HCF(66,6) = HCF(138,66) = HCF(204,138) = HCF(342,204) = HCF(888,342) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 720 > 6, we apply the division lemma to 720 and 6, to get
720 = 6 x 120 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 720 is 6
Notice that 6 = HCF(720,6) .
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Frequently Asked Questions on HCF of 888, 342, 720 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, 342, 720?
Answer: HCF of 888, 342, 720 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 888, 342, 720 using Euclid's Algorithm?
Answer: For arbitrary numbers 888, 342, 720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.