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, 800, 438 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 800, 438 is 2 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, 800, 438 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, 800, 438 is 2.
HCF(450, 800, 438) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 450, 800, 438 is 2.
Step 1: Since 800 > 450, we apply the division lemma to 800 and 450, to get
800 = 450 x 1 + 350
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 350 and 450, to get
450 = 350 x 1 + 100
Step 3: We consider the new divisor 350 and the new remainder 100, and apply the division lemma to get
350 = 100 x 3 + 50
We consider the new divisor 100 and the new remainder 50, and apply the division lemma to get
100 = 50 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 50, the HCF of 450 and 800 is 50
Notice that 50 = HCF(100,50) = HCF(350,100) = HCF(450,350) = HCF(800,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 438 > 50, we apply the division lemma to 438 and 50, to get
438 = 50 x 8 + 38
Step 2: Since the reminder 50 ≠ 0, we apply division lemma to 38 and 50, to get
50 = 38 x 1 + 12
Step 3: We consider the new divisor 38 and the new remainder 12, and apply the division lemma to get
38 = 12 x 3 + 2
We consider the new divisor 12 and the new remainder 2, and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 50 and 438 is 2
Notice that 2 = HCF(12,2) = HCF(38,12) = HCF(50,38) = HCF(438,50) .
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, 800, 438?
Answer: HCF of 450, 800, 438 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 800, 438 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 800, 438 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.