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, 745, 973 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 745, 973 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, 745, 973 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, 745, 973 is 1.
HCF(450, 745, 973) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 450, 745, 973 is 1.
Step 1: Since 745 > 450, we apply the division lemma to 745 and 450, to get
745 = 450 x 1 + 295
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 295 and 450, to get
450 = 295 x 1 + 155
Step 3: We consider the new divisor 295 and the new remainder 155, and apply the division lemma to get
295 = 155 x 1 + 140
We consider the new divisor 155 and the new remainder 140,and apply the division lemma to get
155 = 140 x 1 + 15
We consider the new divisor 140 and the new remainder 15,and apply the division lemma to get
140 = 15 x 9 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 450 and 745 is 5
Notice that 5 = HCF(15,5) = HCF(140,15) = HCF(155,140) = HCF(295,155) = HCF(450,295) = HCF(745,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 973 > 5, we apply the division lemma to 973 and 5, to get
973 = 5 x 194 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 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 5 and 973 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(973,5) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 745, 973?
Answer: HCF of 450, 745, 973 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 745, 973 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 745, 973 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.