Highest Common Factor of 1640, 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 1640, 450 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 1640, 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 1640, 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 1640, 450 is 10.
HCF(1640, 450) = 10
HCF of 1640, 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 1640, 450 is 10.
Highest Common Factor of 1640,450 is 10
Step 1: Since 1640 > 450, we apply the division lemma to 1640 and 450, to get
1640 = 450 x 3 + 290
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 290 and 450, to get
450 = 290 x 1 + 160
Step 3: We consider the new divisor 290 and the new remainder 160, and apply the division lemma to get
290 = 160 x 1 + 130
We consider the new divisor 160 and the new remainder 130,and apply the division lemma to get
160 = 130 x 1 + 30
We consider the new divisor 130 and the new remainder 30,and apply the division lemma to get
130 = 30 x 4 + 10
We consider the new divisor 30 and the new remainder 10,and apply the division lemma to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 1640 and 450 is 10
Notice that 10 = HCF(30,10) = HCF(130,30) = HCF(160,130) = HCF(290,160) = HCF(450,290) = HCF(1640,450) .
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Frequently Asked Questions on HCF of 1640, 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 1640, 450?
Answer: HCF of 1640, 450 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1640, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 1640, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
