Highest Common Factor of 450, 760, 832 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, 760, 832 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 760, 832 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, 760, 832 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, 760, 832 is 2.
HCF(450, 760, 832) = 2
HCF of 450, 760, 832 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, 760, 832 is 2.
Highest Common Factor of 450,760,832 is 2
Step 1: Since 760 > 450, we apply the division lemma to 760 and 450, to get
760 = 450 x 1 + 310
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 310 and 450, to get
450 = 310 x 1 + 140
Step 3: We consider the new divisor 310 and the new remainder 140, and apply the division lemma to get
310 = 140 x 2 + 30
We consider the new divisor 140 and the new remainder 30,and apply the division lemma to get
140 = 30 x 4 + 20
We consider the new divisor 30 and the new remainder 20,and apply the division lemma to get
30 = 20 x 1 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 450 and 760 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(140,30) = HCF(310,140) = HCF(450,310) = HCF(760,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 832 > 10, we apply the division lemma to 832 and 10, to get
832 = 10 x 83 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 832 is 2
Notice that 2 = HCF(10,2) = HCF(832,10) .
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Frequently Asked Questions on HCF of 450, 760, 832 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, 760, 832?
Answer: HCF of 450, 760, 832 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 760, 832 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 760, 832 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.