Highest Common Factor of 54, 138, 560, 588 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 54, 138, 560, 588 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 54, 138, 560, 588 is 2 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 54, 138, 560, 588 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 54, 138, 560, 588 is 2.
HCF(54, 138, 560, 588) = 2
HCF of 54, 138, 560, 588 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 54, 138, 560, 588 is 2.
Highest Common Factor of 54,138,560,588 is 2
Step 1: Since 138 > 54, we apply the division lemma to 138 and 54, to get
138 = 54 x 2 + 30
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 30 and 54, to get
54 = 30 x 1 + 24
Step 3: We consider the new divisor 30 and the new remainder 24, and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 54 and 138 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(54,30) = HCF(138,54) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 560 > 6, we apply the division lemma to 560 and 6, to get
560 = 6 x 93 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 560 is 2
Notice that 2 = HCF(6,2) = HCF(560,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 588 > 2, we apply the division lemma to 588 and 2, to get
588 = 2 x 294 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 588 is 2
Notice that 2 = HCF(588,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 54, 138, 560, 588 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 54, 138, 560, 588?
Answer: HCF of 54, 138, 560, 588 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 54, 138, 560, 588 using Euclid's Algorithm?
Answer: For arbitrary numbers 54, 138, 560, 588 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.