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 722, 450 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 722, 450 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 722, 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 722, 450 is 2.
HCF(722, 450) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 722, 450 is 2.
Step 1: Since 722 > 450, we apply the division lemma to 722 and 450, to get
722 = 450 x 1 + 272
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 272 and 450, to get
450 = 272 x 1 + 178
Step 3: We consider the new divisor 272 and the new remainder 178, and apply the division lemma to get
272 = 178 x 1 + 94
We consider the new divisor 178 and the new remainder 94,and apply the division lemma to get
178 = 94 x 1 + 84
We consider the new divisor 94 and the new remainder 84,and apply the division lemma to get
94 = 84 x 1 + 10
We consider the new divisor 84 and the new remainder 10,and apply the division lemma to get
84 = 10 x 8 + 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 722 and 450 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(84,10) = HCF(94,84) = HCF(178,94) = HCF(272,178) = HCF(450,272) = HCF(722,450) .
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 722, 450?
Answer: HCF of 722, 450 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 722, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 722, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.