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 305, 1098, 8008 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 305, 1098, 8008 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 305, 1098, 8008 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 305, 1098, 8008 is 1.
HCF(305, 1098, 8008) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 305, 1098, 8008 is 1.
Step 1: Since 1098 > 305, we apply the division lemma to 1098 and 305, to get
1098 = 305 x 3 + 183
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 183 and 305, to get
305 = 183 x 1 + 122
Step 3: We consider the new divisor 183 and the new remainder 122, and apply the division lemma to get
183 = 122 x 1 + 61
We consider the new divisor 122 and the new remainder 61, and apply the division lemma to get
122 = 61 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 61, the HCF of 305 and 1098 is 61
Notice that 61 = HCF(122,61) = HCF(183,122) = HCF(305,183) = HCF(1098,305) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8008 > 61, we apply the division lemma to 8008 and 61, to get
8008 = 61 x 131 + 17
Step 2: Since the reminder 61 ≠ 0, we apply division lemma to 17 and 61, to get
61 = 17 x 3 + 10
Step 3: 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 61 and 8008 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(61,17) = HCF(8008,61) .
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 305, 1098, 8008?
Answer: HCF of 305, 1098, 8008 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 305, 1098, 8008 using Euclid's Algorithm?
Answer: For arbitrary numbers 305, 1098, 8008 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.