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 726, 450 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 726, 450 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 726, 450 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 726, 450 is 6.
HCF(726, 450) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 726, 450 is 6.
Step 1: Since 726 > 450, we apply the division lemma to 726 and 450, to get
726 = 450 x 1 + 276
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 276 and 450, to get
450 = 276 x 1 + 174
Step 3: We consider the new divisor 276 and the new remainder 174, and apply the division lemma to get
276 = 174 x 1 + 102
We consider the new divisor 174 and the new remainder 102,and apply the division lemma to get
174 = 102 x 1 + 72
We consider the new divisor 102 and the new remainder 72,and apply the division lemma to get
102 = 72 x 1 + 30
We consider the new divisor 72 and the new remainder 30,and apply the division lemma to get
72 = 30 x 2 + 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 726 and 450 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(72,30) = HCF(102,72) = HCF(174,102) = HCF(276,174) = HCF(450,276) = HCF(726,450) .
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 726, 450?
Answer: HCF of 726, 450 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 726, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 726, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.