Highest Common Factor of 504, 288, 39 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 504, 288, 39 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 288, 39 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 504, 288, 39 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 504, 288, 39 is 3.
HCF(504, 288, 39) = 3
HCF of 504, 288, 39 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 288, 39 is 3.
Highest Common Factor of 504,288,39 is 3
Step 1: Since 504 > 288, we apply the division lemma to 504 and 288, to get
504 = 288 x 1 + 216
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 216 and 288, to get
288 = 216 x 1 + 72
Step 3: We consider the new divisor 216 and the new remainder 72, and apply the division lemma to get
216 = 72 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 72, the HCF of 504 and 288 is 72
Notice that 72 = HCF(216,72) = HCF(288,216) = HCF(504,288) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 72 > 39, we apply the division lemma to 72 and 39, to get
72 = 39 x 1 + 33
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 33 and 39, to get
39 = 33 x 1 + 6
Step 3: We consider the new divisor 33 and the new remainder 6, and apply the division lemma to get
33 = 6 x 5 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 72 and 39 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(72,39) .
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Frequently Asked Questions on HCF of 504, 288, 39 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 504, 288, 39?
Answer: HCF of 504, 288, 39 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 288, 39 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 288, 39 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.