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 288, 744, 398 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 288, 744, 398 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 288, 744, 398 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 288, 744, 398 is 2.
HCF(288, 744, 398) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 288, 744, 398 is 2.
Step 1: Since 744 > 288, we apply the division lemma to 744 and 288, to get
744 = 288 x 2 + 168
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 168 and 288, to get
288 = 168 x 1 + 120
Step 3: We consider the new divisor 168 and the new remainder 120, and apply the division lemma to get
168 = 120 x 1 + 48
We consider the new divisor 120 and the new remainder 48,and apply the division lemma to get
120 = 48 x 2 + 24
We consider the new divisor 48 and the new remainder 24,and apply the division lemma to get
48 = 24 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 288 and 744 is 24
Notice that 24 = HCF(48,24) = HCF(120,48) = HCF(168,120) = HCF(288,168) = HCF(744,288) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 398 > 24, we apply the division lemma to 398 and 24, to get
398 = 24 x 16 + 14
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 14 and 24, to get
24 = 14 x 1 + 10
Step 3: We consider the new divisor 14 and the new remainder 10, and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 24 and 398 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(398,24) .
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 288, 744, 398?
Answer: HCF of 288, 744, 398 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 288, 744, 398 using Euclid's Algorithm?
Answer: For arbitrary numbers 288, 744, 398 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.