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, 983, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 722, 983, 213 is 1 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, 983, 213 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, 983, 213 is 1.
HCF(722, 983, 213) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 722, 983, 213 is 1.
Step 1: Since 983 > 722, we apply the division lemma to 983 and 722, to get
983 = 722 x 1 + 261
Step 2: Since the reminder 722 ≠ 0, we apply division lemma to 261 and 722, to get
722 = 261 x 2 + 200
Step 3: We consider the new divisor 261 and the new remainder 200, and apply the division lemma to get
261 = 200 x 1 + 61
We consider the new divisor 200 and the new remainder 61,and apply the division lemma to get
200 = 61 x 3 + 17
We consider the new divisor 61 and the new remainder 17,and apply the division lemma to get
61 = 17 x 3 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 722 and 983 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(61,17) = HCF(200,61) = HCF(261,200) = HCF(722,261) = HCF(983,722) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 213 > 1, we apply the division lemma to 213 and 1, to get
213 = 1 x 213 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 213 is 1
Notice that 1 = HCF(213,1) .
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, 983, 213?
Answer: HCF of 722, 983, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 722, 983, 213 using Euclid's Algorithm?
Answer: For arbitrary numbers 722, 983, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.