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, 7104 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 7104 is 6 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, 7104 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, 7104 is 6.
HCF(450, 7104) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 450, 7104 is 6.
Step 1: Since 7104 > 450, we apply the division lemma to 7104 and 450, to get
7104 = 450 x 15 + 354
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 354 and 450, to get
450 = 354 x 1 + 96
Step 3: We consider the new divisor 354 and the new remainder 96, and apply the division lemma to get
354 = 96 x 3 + 66
We consider the new divisor 96 and the new remainder 66,and apply the division lemma to get
96 = 66 x 1 + 30
We consider the new divisor 66 and the new remainder 30,and apply the division lemma to get
66 = 30 x 2 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 450 and 7104 is 6
Notice that 6 = HCF(30,6) = HCF(66,30) = HCF(96,66) = HCF(354,96) = HCF(450,354) = HCF(7104,450) .
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, 7104?
Answer: HCF of 450, 7104 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 7104 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 7104 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.