Highest Common Factor of 450, 765 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, 765 i.e. 45 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 765 is 45 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, 765 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, 765 is 45.
HCF(450, 765) = 45
HCF of 450, 765 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, 765 is 45.
Highest Common Factor of 450,765 is 45
Step 1: Since 765 > 450, we apply the division lemma to 765 and 450, to get
765 = 450 x 1 + 315
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 315 and 450, to get
450 = 315 x 1 + 135
Step 3: We consider the new divisor 315 and the new remainder 135, and apply the division lemma to get
315 = 135 x 2 + 45
We consider the new divisor 135 and the new remainder 45, and apply the division lemma to get
135 = 45 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 450 and 765 is 45
Notice that 45 = HCF(135,45) = HCF(315,135) = HCF(450,315) = HCF(765,450) .
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Frequently Asked Questions on HCF of 450, 765 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, 765?
Answer: HCF of 450, 765 is 45 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.