Highest Common Factor of 576, 138, 708 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 576, 138, 708 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 576, 138, 708 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 576, 138, 708 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 576, 138, 708 is 6.
HCF(576, 138, 708) = 6
HCF of 576, 138, 708 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 576, 138, 708 is 6.
Highest Common Factor of 576,138,708 is 6
Step 1: Since 576 > 138, we apply the division lemma to 576 and 138, to get
576 = 138 x 4 + 24
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 24 and 138, to get
138 = 24 x 5 + 18
Step 3: We consider the new divisor 24 and the new remainder 18, and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6, and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 576 and 138 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(138,24) = HCF(576,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 708 > 6, we apply the division lemma to 708 and 6, to get
708 = 6 x 118 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 708 is 6
Notice that 6 = HCF(708,6) .
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Frequently Asked Questions on HCF of 576, 138, 708 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 576, 138, 708?
Answer: HCF of 576, 138, 708 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 576, 138, 708 using Euclid's Algorithm?
Answer: For arbitrary numbers 576, 138, 708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
