Highest Common Factor of 240, 685, 530, 23 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 240, 685, 530, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 240, 685, 530, 23 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 240, 685, 530, 23 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 240, 685, 530, 23 is 1.
HCF(240, 685, 530, 23) = 1
HCF of 240, 685, 530, 23 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 240, 685, 530, 23 is 1.
Highest Common Factor of 240,685,530,23 is 1
Step 1: Since 685 > 240, we apply the division lemma to 685 and 240, to get
685 = 240 x 2 + 205
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 205 and 240, to get
240 = 205 x 1 + 35
Step 3: We consider the new divisor 205 and the new remainder 35, and apply the division lemma to get
205 = 35 x 5 + 30
We consider the new divisor 35 and the new remainder 30,and apply the division lemma to get
35 = 30 x 1 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 240 and 685 is 5
Notice that 5 = HCF(30,5) = HCF(35,30) = HCF(205,35) = HCF(240,205) = HCF(685,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 530 > 5, we apply the division lemma to 530 and 5, to get
530 = 5 x 106 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 530 is 5
Notice that 5 = HCF(530,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 23 > 5, we apply the division lemma to 23 and 5, to get
23 = 5 x 4 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 23 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) .
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Frequently Asked Questions on HCF of 240, 685, 530, 23 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 240, 685, 530, 23?
Answer: HCF of 240, 685, 530, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 240, 685, 530, 23 using Euclid's Algorithm?
Answer: For arbitrary numbers 240, 685, 530, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.