Highest Common Factor of 240, 589, 688 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, 589, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 240, 589, 688 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, 589, 688 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, 589, 688 is 1.
HCF(240, 589, 688) = 1
HCF of 240, 589, 688 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, 589, 688 is 1.
Highest Common Factor of 240,589,688 is 1
Step 1: Since 589 > 240, we apply the division lemma to 589 and 240, to get
589 = 240 x 2 + 109
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 109 and 240, to get
240 = 109 x 2 + 22
Step 3: We consider the new divisor 109 and the new remainder 22, and apply the division lemma to get
109 = 22 x 4 + 21
We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get
22 = 21 x 1 + 1
We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 240 and 589 is 1
Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(109,22) = HCF(240,109) = HCF(589,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 688 > 1, we apply the division lemma to 688 and 1, to get
688 = 1 x 688 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 688 is 1
Notice that 1 = HCF(688,1) .
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Frequently Asked Questions on HCF of 240, 589, 688 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, 589, 688?
Answer: HCF of 240, 589, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 240, 589, 688 using Euclid's Algorithm?
Answer: For arbitrary numbers 240, 589, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.