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 980, 769, 113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 980, 769, 113 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 980, 769, 113 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 980, 769, 113 is 1.
HCF(980, 769, 113) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 980, 769, 113 is 1.
Step 1: Since 980 > 769, we apply the division lemma to 980 and 769, to get
980 = 769 x 1 + 211
Step 2: Since the reminder 769 ≠ 0, we apply division lemma to 211 and 769, to get
769 = 211 x 3 + 136
Step 3: We consider the new divisor 211 and the new remainder 136, and apply the division lemma to get
211 = 136 x 1 + 75
We consider the new divisor 136 and the new remainder 75,and apply the division lemma to get
136 = 75 x 1 + 61
We consider the new divisor 75 and the new remainder 61,and apply the division lemma to get
75 = 61 x 1 + 14
We consider the new divisor 61 and the new remainder 14,and apply the division lemma to get
61 = 14 x 4 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 980 and 769 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(61,14) = HCF(75,61) = HCF(136,75) = HCF(211,136) = HCF(769,211) = HCF(980,769) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 113 > 1, we apply the division lemma to 113 and 1, to get
113 = 1 x 113 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 113 is 1
Notice that 1 = HCF(113,1) .
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 980, 769, 113?
Answer: HCF of 980, 769, 113 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 980, 769, 113 using Euclid's Algorithm?
Answer: For arbitrary numbers 980, 769, 113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.