Highest Common Factor of 340, 450, 403 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, 450, 403 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 450, 403 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 340, 450, 403 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, 450, 403 is 1.
HCF(340, 450, 403) = 1
HCF of 340, 450, 403 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, 450, 403 is 1.
Highest Common Factor of 340,450,403 is 1
Step 1: Since 450 > 340, we apply the division lemma to 450 and 340, to get
450 = 340 x 1 + 110
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 110 and 340, to get
340 = 110 x 3 + 10
Step 3: We consider the new divisor 110 and the new remainder 10, and apply the division lemma to get
110 = 10 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 340 and 450 is 10
Notice that 10 = HCF(110,10) = HCF(340,110) = HCF(450,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 403 > 10, we apply the division lemma to 403 and 10, to get
403 = 10 x 40 + 3
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 3 and 10, to get
10 = 3 x 3 + 1
Step 3: 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 10 and 403 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(403,10) .
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Frequently Asked Questions on HCF of 340, 450, 403 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, 450, 403?
Answer: HCF of 340, 450, 403 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 450, 403 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 450, 403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.