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 705, 500, 492 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 500, 492 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 705, 500, 492 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 705, 500, 492 is 1.
HCF(705, 500, 492) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 500, 492 is 1.
Step 1: Since 705 > 500, we apply the division lemma to 705 and 500, to get
705 = 500 x 1 + 205
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 205 and 500, to get
500 = 205 x 2 + 90
Step 3: We consider the new divisor 205 and the new remainder 90, and apply the division lemma to get
205 = 90 x 2 + 25
We consider the new divisor 90 and the new remainder 25,and apply the division lemma to get
90 = 25 x 3 + 15
We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 705 and 500 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(90,25) = HCF(205,90) = HCF(500,205) = HCF(705,500) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 492 > 5, we apply the division lemma to 492 and 5, to get
492 = 5 x 98 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 492 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(492,5) .
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 705, 500, 492?
Answer: HCF of 705, 500, 492 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 500, 492 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 500, 492 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.