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 453, 720, 577 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 453, 720, 577 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 453, 720, 577 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 453, 720, 577 is 1.
HCF(453, 720, 577) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 453, 720, 577 is 1.
Step 1: Since 720 > 453, we apply the division lemma to 720 and 453, to get
720 = 453 x 1 + 267
Step 2: Since the reminder 453 ≠ 0, we apply division lemma to 267 and 453, to get
453 = 267 x 1 + 186
Step 3: We consider the new divisor 267 and the new remainder 186, and apply the division lemma to get
267 = 186 x 1 + 81
We consider the new divisor 186 and the new remainder 81,and apply the division lemma to get
186 = 81 x 2 + 24
We consider the new divisor 81 and the new remainder 24,and apply the division lemma to get
81 = 24 x 3 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 453 and 720 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(81,24) = HCF(186,81) = HCF(267,186) = HCF(453,267) = HCF(720,453) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 577 > 3, we apply the division lemma to 577 and 3, to get
577 = 3 x 192 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 577 is 1
Notice that 1 = HCF(3,1) = HCF(577,3) .
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 453, 720, 577?
Answer: HCF of 453, 720, 577 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 453, 720, 577 using Euclid's Algorithm?
Answer: For arbitrary numbers 453, 720, 577 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.