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 903, 559, 326, 197 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 903, 559, 326, 197 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 903, 559, 326, 197 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 903, 559, 326, 197 is 1.
HCF(903, 559, 326, 197) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 903, 559, 326, 197 is 1.
Step 1: Since 903 > 559, we apply the division lemma to 903 and 559, to get
903 = 559 x 1 + 344
Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 344 and 559, to get
559 = 344 x 1 + 215
Step 3: We consider the new divisor 344 and the new remainder 215, and apply the division lemma to get
344 = 215 x 1 + 129
We consider the new divisor 215 and the new remainder 129,and apply the division lemma to get
215 = 129 x 1 + 86
We consider the new divisor 129 and the new remainder 86,and apply the division lemma to get
129 = 86 x 1 + 43
We consider the new divisor 86 and the new remainder 43,and apply the division lemma to get
86 = 43 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 903 and 559 is 43
Notice that 43 = HCF(86,43) = HCF(129,86) = HCF(215,129) = HCF(344,215) = HCF(559,344) = HCF(903,559) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 326 > 43, we apply the division lemma to 326 and 43, to get
326 = 43 x 7 + 25
Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 25 and 43, to get
43 = 25 x 1 + 18
Step 3: We consider the new divisor 25 and the new remainder 18, and apply the division lemma to get
25 = 18 x 1 + 7
We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get
18 = 7 x 2 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 43 and 326 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(25,18) = HCF(43,25) = HCF(326,43) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 197 > 1, we apply the division lemma to 197 and 1, to get
197 = 1 x 197 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 197 is 1
Notice that 1 = HCF(197,1) .
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 903, 559, 326, 197?
Answer: HCF of 903, 559, 326, 197 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 903, 559, 326, 197 using Euclid's Algorithm?
Answer: For arbitrary numbers 903, 559, 326, 197 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.