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 490, 775, 396 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 490, 775, 396 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 490, 775, 396 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 490, 775, 396 is 1.
HCF(490, 775, 396) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 490, 775, 396 is 1.
Step 1: Since 775 > 490, we apply the division lemma to 775 and 490, to get
775 = 490 x 1 + 285
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 285 and 490, to get
490 = 285 x 1 + 205
Step 3: We consider the new divisor 285 and the new remainder 205, and apply the division lemma to get
285 = 205 x 1 + 80
We consider the new divisor 205 and the new remainder 80,and apply the division lemma to get
205 = 80 x 2 + 45
We consider the new divisor 80 and the new remainder 45,and apply the division lemma to get
80 = 45 x 1 + 35
We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get
45 = 35 x 1 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 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 490 and 775 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(80,45) = HCF(205,80) = HCF(285,205) = HCF(490,285) = HCF(775,490) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 396 > 5, we apply the division lemma to 396 and 5, to get
396 = 5 x 79 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 396 is 1
Notice that 1 = HCF(5,1) = HCF(396,5) .
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 490, 775, 396?
Answer: HCF of 490, 775, 396 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 490, 775, 396 using Euclid's Algorithm?
Answer: For arbitrary numbers 490, 775, 396 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.