Highest Common Factor of 450, 700, 769 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, 700, 769 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 700, 769 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, 700, 769 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, 700, 769 is 1.
HCF(450, 700, 769) = 1
HCF of 450, 700, 769 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, 700, 769 is 1.
Highest Common Factor of 450,700,769 is 1
Step 1: Since 700 > 450, we apply the division lemma to 700 and 450, to get
700 = 450 x 1 + 250
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 250 and 450, to get
450 = 250 x 1 + 200
Step 3: We consider the new divisor 250 and the new remainder 200, and apply the division lemma to get
250 = 200 x 1 + 50
We consider the new divisor 200 and the new remainder 50, and apply the division lemma to get
200 = 50 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 50, the HCF of 450 and 700 is 50
Notice that 50 = HCF(200,50) = HCF(250,200) = HCF(450,250) = HCF(700,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 769 > 50, we apply the division lemma to 769 and 50, to get
769 = 50 x 15 + 19
Step 2: Since the reminder 50 ≠ 0, we apply division lemma to 19 and 50, to get
50 = 19 x 2 + 12
Step 3: We consider the new divisor 19 and the new remainder 12, and apply the division lemma to get
19 = 12 x 1 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 50 and 769 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(50,19) = HCF(769,50) .
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Frequently Asked Questions on HCF of 450, 700, 769 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, 700, 769?
Answer: HCF of 450, 700, 769 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 700, 769 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 700, 769 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.