Highest Common Factor of 288, 996, 878 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 288, 996, 878 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 288, 996, 878 is 2 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 288, 996, 878 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 288, 996, 878 is 2.
HCF(288, 996, 878) = 2
HCF of 288, 996, 878 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 288, 996, 878 is 2.
Highest Common Factor of 288,996,878 is 2
Step 1: Since 996 > 288, we apply the division lemma to 996 and 288, to get
996 = 288 x 3 + 132
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 132 and 288, to get
288 = 132 x 2 + 24
Step 3: We consider the new divisor 132 and the new remainder 24, and apply the division lemma to get
132 = 24 x 5 + 12
We consider the new divisor 24 and the new remainder 12, and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 288 and 996 is 12
Notice that 12 = HCF(24,12) = HCF(132,24) = HCF(288,132) = HCF(996,288) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 878 > 12, we apply the division lemma to 878 and 12, to get
878 = 12 x 73 + 2
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 2 and 12, to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 878 is 2
Notice that 2 = HCF(12,2) = HCF(878,12) .
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Frequently Asked Questions on HCF of 288, 996, 878 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 288, 996, 878?
Answer: HCF of 288, 996, 878 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 288, 996, 878 using Euclid's Algorithm?
Answer: For arbitrary numbers 288, 996, 878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.