Highest Common Factor of 270, 340, 450 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 270, 340, 450 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 340, 450 is 10 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 270, 340, 450 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 270, 340, 450 is 10.
HCF(270, 340, 450) = 10
HCF of 270, 340, 450 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 270, 340, 450 is 10.
Highest Common Factor of 270,340,450 is 10
Step 1: Since 340 > 270, we apply the division lemma to 340 and 270, to get
340 = 270 x 1 + 70
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 70 and 270, to get
270 = 70 x 3 + 60
Step 3: We consider the new divisor 70 and the new remainder 60, and apply the division lemma to get
70 = 60 x 1 + 10
We consider the new divisor 60 and the new remainder 10, and apply the division lemma to get
60 = 10 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 270 and 340 is 10
Notice that 10 = HCF(60,10) = HCF(70,60) = HCF(270,70) = HCF(340,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 450 > 10, we apply the division lemma to 450 and 10, to get
450 = 10 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 10 and 450 is 10
Notice that 10 = HCF(450,10) .
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Frequently Asked Questions on HCF of 270, 340, 450 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 270, 340, 450?
Answer: HCF of 270, 340, 450 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 340, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 340, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
