Highest Common Factor of 578, 309, 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 578, 309, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 309, 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 578, 309, 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 578, 309, 688 is 1.
HCF(578, 309, 688) = 1
HCF of 578, 309, 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 578, 309, 688 is 1.
Highest Common Factor of 578,309,688 is 1
Step 1: Since 578 > 309, we apply the division lemma to 578 and 309, to get
578 = 309 x 1 + 269
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 269 and 309, to get
309 = 269 x 1 + 40
Step 3: We consider the new divisor 269 and the new remainder 40, and apply the division lemma to get
269 = 40 x 6 + 29
We consider the new divisor 40 and the new remainder 29,and apply the division lemma to get
40 = 29 x 1 + 11
We consider the new divisor 29 and the new remainder 11,and apply the division lemma to get
29 = 11 x 2 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 578 and 309 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(29,11) = HCF(40,29) = HCF(269,40) = HCF(309,269) = HCF(578,309) .
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 578, 309, 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 578, 309, 688?
Answer: HCF of 578, 309, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 309, 688 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 309, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.