Highest Common Factor of 546, 744, 30 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 546, 744, 30 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 744, 30 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 546, 744, 30 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 546, 744, 30 is 6.
HCF(546, 744, 30) = 6
HCF of 546, 744, 30 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 546, 744, 30 is 6.
Highest Common Factor of 546,744,30 is 6
Step 1: Since 744 > 546, we apply the division lemma to 744 and 546, to get
744 = 546 x 1 + 198
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 198 and 546, to get
546 = 198 x 2 + 150
Step 3: We consider the new divisor 198 and the new remainder 150, and apply the division lemma to get
198 = 150 x 1 + 48
We consider the new divisor 150 and the new remainder 48,and apply the division lemma to get
150 = 48 x 3 + 6
We consider the new divisor 48 and the new remainder 6,and apply the division lemma to get
48 = 6 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 546 and 744 is 6
Notice that 6 = HCF(48,6) = HCF(150,48) = HCF(198,150) = HCF(546,198) = HCF(744,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30 > 6, we apply the division lemma to 30 and 6, to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 30 is 6
Notice that 6 = HCF(30,6) .
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Frequently Asked Questions on HCF of 546, 744, 30 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 546, 744, 30?
Answer: HCF of 546, 744, 30 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 744, 30 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 744, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.