Highest Common Factor of 978, 576, 732 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 978, 576, 732 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 576, 732 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 978, 576, 732 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 978, 576, 732 is 6.
HCF(978, 576, 732) = 6
HCF of 978, 576, 732 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 576, 732 is 6.
Highest Common Factor of 978,576,732 is 6
Step 1: Since 978 > 576, we apply the division lemma to 978 and 576, to get
978 = 576 x 1 + 402
Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 402 and 576, to get
576 = 402 x 1 + 174
Step 3: We consider the new divisor 402 and the new remainder 174, and apply the division lemma to get
402 = 174 x 2 + 54
We consider the new divisor 174 and the new remainder 54,and apply the division lemma to get
174 = 54 x 3 + 12
We consider the new divisor 54 and the new remainder 12,and apply the division lemma to get
54 = 12 x 4 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 978 and 576 is 6
Notice that 6 = HCF(12,6) = HCF(54,12) = HCF(174,54) = HCF(402,174) = HCF(576,402) = HCF(978,576) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 732 > 6, we apply the division lemma to 732 and 6, to get
732 = 6 x 122 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 732 is 6
Notice that 6 = HCF(732,6) .
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Frequently Asked Questions on HCF of 978, 576, 732 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 978, 576, 732?
Answer: HCF of 978, 576, 732 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 576, 732 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 576, 732 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.