Highest Common Factor of 288, 252, 960 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, 252, 960 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 288, 252, 960 is 12 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, 252, 960 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, 252, 960 is 12.
HCF(288, 252, 960) = 12
HCF of 288, 252, 960 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, 252, 960 is 12.
Highest Common Factor of 288,252,960 is 12
Step 1: Since 288 > 252, we apply the division lemma to 288 and 252, to get
288 = 252 x 1 + 36
Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 36 and 252, to get
252 = 36 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 288 and 252 is 36
Notice that 36 = HCF(252,36) = HCF(288,252) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 960 > 36, we apply the division lemma to 960 and 36, to get
960 = 36 x 26 + 24
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 24 and 36, to get
36 = 24 x 1 + 12
Step 3: 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 36 and 960 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(960,36) .
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Frequently Asked Questions on HCF of 288, 252, 960 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, 252, 960?
Answer: HCF of 288, 252, 960 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 288, 252, 960 using Euclid's Algorithm?
Answer: For arbitrary numbers 288, 252, 960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.