Highest Common Factor of 450, 730, 767 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, 730, 767 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 730, 767 is 1 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, 730, 767 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, 730, 767 is 1.
HCF(450, 730, 767) = 1
HCF of 450, 730, 767 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, 730, 767 is 1.
Highest Common Factor of 450,730,767 is 1
Step 1: Since 730 > 450, we apply the division lemma to 730 and 450, to get
730 = 450 x 1 + 280
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 280 and 450, to get
450 = 280 x 1 + 170
Step 3: We consider the new divisor 280 and the new remainder 170, and apply the division lemma to get
280 = 170 x 1 + 110
We consider the new divisor 170 and the new remainder 110,and apply the division lemma to get
170 = 110 x 1 + 60
We consider the new divisor 110 and the new remainder 60,and apply the division lemma to get
110 = 60 x 1 + 50
We consider the new divisor 60 and the new remainder 50,and apply the division lemma to get
60 = 50 x 1 + 10
We consider the new divisor 50 and the new remainder 10,and apply the division lemma to get
50 = 10 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 450 and 730 is 10
Notice that 10 = HCF(50,10) = HCF(60,50) = HCF(110,60) = HCF(170,110) = HCF(280,170) = HCF(450,280) = HCF(730,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 767 > 10, we apply the division lemma to 767 and 10, to get
767 = 10 x 76 + 7
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 7 and 10, to get
10 = 7 x 1 + 3
Step 3: We consider the new divisor 7 and the new remainder 3, and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 767 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(767,10) .
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Frequently Asked Questions on HCF of 450, 730, 767 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, 730, 767?
Answer: HCF of 450, 730, 767 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 730, 767 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 730, 767 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.