Highest Common Factor of 384, 654, 55 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 384, 654, 55 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 384, 654, 55 is 1 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 384, 654, 55 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 384, 654, 55 is 1.
HCF(384, 654, 55) = 1
HCF of 384, 654, 55 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 384, 654, 55 is 1.
Highest Common Factor of 384,654,55 is 1
Step 1: Since 654 > 384, we apply the division lemma to 654 and 384, to get
654 = 384 x 1 + 270
Step 2: Since the reminder 384 ≠ 0, we apply division lemma to 270 and 384, to get
384 = 270 x 1 + 114
Step 3: We consider the new divisor 270 and the new remainder 114, and apply the division lemma to get
270 = 114 x 2 + 42
We consider the new divisor 114 and the new remainder 42,and apply the division lemma to get
114 = 42 x 2 + 30
We consider the new divisor 42 and the new remainder 30,and apply the division lemma to get
42 = 30 x 1 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 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 384 and 654 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(114,42) = HCF(270,114) = HCF(384,270) = HCF(654,384) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55 > 6, we apply the division lemma to 55 and 6, to get
55 = 6 x 9 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 55 is 1
Notice that 1 = HCF(6,1) = HCF(55,6) .
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Frequently Asked Questions on HCF of 384, 654, 55 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 384, 654, 55?
Answer: HCF of 384, 654, 55 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 384, 654, 55 using Euclid's Algorithm?
Answer: For arbitrary numbers 384, 654, 55 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.