Highest Common Factor of 450, 502 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 450, 502 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 502 is 2 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 450, 502 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 450, 502 is 2.
HCF(450, 502) = 2
HCF of 450, 502 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 450, 502 is 2.
Highest Common Factor of 450,502 is 2
Step 1: Since 502 > 450, we apply the division lemma to 502 and 450, to get
502 = 450 x 1 + 52
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 52 and 450, to get
450 = 52 x 8 + 34
Step 3: We consider the new divisor 52 and the new remainder 34, and apply the division lemma to get
52 = 34 x 1 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 450 and 502 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(52,34) = HCF(450,52) = HCF(502,450) .
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Frequently Asked Questions on HCF of 450, 502 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 450, 502?
Answer: HCF of 450, 502 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 502 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 502 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.