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 1119, 1996 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1119, 1996 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 1119, 1996 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 1119, 1996 is 1.
HCF(1119, 1996) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1119, 1996 is 1.
Step 1: Since 1996 > 1119, we apply the division lemma to 1996 and 1119, to get
1996 = 1119 x 1 + 877
Step 2: Since the reminder 1119 ≠ 0, we apply division lemma to 877 and 1119, to get
1119 = 877 x 1 + 242
Step 3: We consider the new divisor 877 and the new remainder 242, and apply the division lemma to get
877 = 242 x 3 + 151
We consider the new divisor 242 and the new remainder 151,and apply the division lemma to get
242 = 151 x 1 + 91
We consider the new divisor 151 and the new remainder 91,and apply the division lemma to get
151 = 91 x 1 + 60
We consider the new divisor 91 and the new remainder 60,and apply the division lemma to get
91 = 60 x 1 + 31
We consider the new divisor 60 and the new remainder 31,and apply the division lemma to get
60 = 31 x 1 + 29
We consider the new divisor 31 and the new remainder 29,and apply the division lemma to get
31 = 29 x 1 + 2
We consider the new divisor 29 and the new remainder 2,and apply the division lemma to get
29 = 2 x 14 + 1
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 1119 and 1996 is 1
Notice that 1 = HCF(2,1) = HCF(29,2) = HCF(31,29) = HCF(60,31) = HCF(91,60) = HCF(151,91) = HCF(242,151) = HCF(877,242) = HCF(1119,877) = HCF(1996,1119) .
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 1119, 1996?
Answer: HCF of 1119, 1996 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1119, 1996 using Euclid's Algorithm?
Answer: For arbitrary numbers 1119, 1996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.