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 723, 988, 263 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 988, 263 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 723, 988, 263 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 723, 988, 263 is 1.
HCF(723, 988, 263) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 723, 988, 263 is 1.
Step 1: Since 988 > 723, we apply the division lemma to 988 and 723, to get
988 = 723 x 1 + 265
Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 265 and 723, to get
723 = 265 x 2 + 193
Step 3: We consider the new divisor 265 and the new remainder 193, and apply the division lemma to get
265 = 193 x 1 + 72
We consider the new divisor 193 and the new remainder 72,and apply the division lemma to get
193 = 72 x 2 + 49
We consider the new divisor 72 and the new remainder 49,and apply the division lemma to get
72 = 49 x 1 + 23
We consider the new divisor 49 and the new remainder 23,and apply the division lemma to get
49 = 23 x 2 + 3
We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get
23 = 3 x 7 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 723 and 988 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(49,23) = HCF(72,49) = HCF(193,72) = HCF(265,193) = HCF(723,265) = HCF(988,723) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 263 > 1, we apply the division lemma to 263 and 1, to get
263 = 1 x 263 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 263 is 1
Notice that 1 = HCF(263,1) .
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 723, 988, 263?
Answer: HCF of 723, 988, 263 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 988, 263 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 988, 263 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.