Highest Common Factor of 340, 459 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 340, 459 i.e. 17 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 459 is 17 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 340, 459 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 340, 459 is 17.
HCF(340, 459) = 17
HCF of 340, 459 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 459 is 17.
Highest Common Factor of 340,459 is 17
Step 1: Since 459 > 340, we apply the division lemma to 459 and 340, to get
459 = 340 x 1 + 119
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 119 and 340, to get
340 = 119 x 2 + 102
Step 3: We consider the new divisor 119 and the new remainder 102, and apply the division lemma to get
119 = 102 x 1 + 17
We consider the new divisor 102 and the new remainder 17, and apply the division lemma to get
102 = 17 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 340 and 459 is 17
Notice that 17 = HCF(102,17) = HCF(119,102) = HCF(340,119) = HCF(459,340) .
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Frequently Asked Questions on HCF of 340, 459 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 340, 459?
Answer: HCF of 340, 459 is 17 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 459 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 459 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.