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 744, 8472 i.e. 24 the largest integer that leaves a remainder zero for all numbers.
HCF of 744, 8472 is 24 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 744, 8472 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 744, 8472 is 24.
HCF(744, 8472) = 24
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 744, 8472 is 24.
Step 1: Since 8472 > 744, we apply the division lemma to 8472 and 744, to get
8472 = 744 x 11 + 288
Step 2: Since the reminder 744 ≠ 0, we apply division lemma to 288 and 744, to get
744 = 288 x 2 + 168
Step 3: We consider the new divisor 288 and the new remainder 168, and apply the division lemma to get
288 = 168 x 1 + 120
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 744 and 8472 is 24
Notice that 24 = HCF(48,24) = HCF(120,48) = HCF(168,120) = HCF(288,168) = HCF(744,288) = HCF(8472,744) .
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 744, 8472?
Answer: HCF of 744, 8472 is 24 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 744, 8472 using Euclid's Algorithm?
Answer: For arbitrary numbers 744, 8472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.