Highest Common Factor of 397, 509, 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 397, 509, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 397, 509, 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 397, 509, 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 397, 509, 688 is 1.
HCF(397, 509, 688) = 1
HCF of 397, 509, 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 397, 509, 688 is 1.
Highest Common Factor of 397,509,688 is 1
Step 1: Since 509 > 397, we apply the division lemma to 509 and 397, to get
509 = 397 x 1 + 112
Step 2: Since the reminder 397 ≠ 0, we apply division lemma to 112 and 397, to get
397 = 112 x 3 + 61
Step 3: We consider the new divisor 112 and the new remainder 61, and apply the division lemma to get
112 = 61 x 1 + 51
We consider the new divisor 61 and the new remainder 51,and apply the division lemma to get
61 = 51 x 1 + 10
We consider the new divisor 51 and the new remainder 10,and apply the division lemma to get
51 = 10 x 5 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 397 and 509 is 1
Notice that 1 = HCF(10,1) = HCF(51,10) = HCF(61,51) = HCF(112,61) = HCF(397,112) = HCF(509,397) .
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 397, 509, 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 397, 509, 688?
Answer: HCF of 397, 509, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 397, 509, 688 using Euclid's Algorithm?
Answer: For arbitrary numbers 397, 509, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.