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, 858, 589 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 858, 589 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, 858, 589 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, 858, 589 is 1.
HCF(450, 858, 589) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 450, 858, 589 is 1.
Step 1: Since 858 > 450, we apply the division lemma to 858 and 450, to get
858 = 450 x 1 + 408
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 408 and 450, to get
450 = 408 x 1 + 42
Step 3: We consider the new divisor 408 and the new remainder 42, and apply the division lemma to get
408 = 42 x 9 + 30
We consider the new divisor 42 and the new remainder 30,and apply the division lemma to get
42 = 30 x 1 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 450 and 858 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(408,42) = HCF(450,408) = HCF(858,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 589 > 6, we apply the division lemma to 589 and 6, to get
589 = 6 x 98 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 589 is 1
Notice that 1 = HCF(6,1) = HCF(589,6) .
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, 858, 589?
Answer: HCF of 450, 858, 589 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 858, 589 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 858, 589 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.