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 1144, 1966 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1144, 1966 is 2 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 1144, 1966 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 1144, 1966 is 2.
HCF(1144, 1966) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1144, 1966 is 2.
Step 1: Since 1966 > 1144, we apply the division lemma to 1966 and 1144, to get
1966 = 1144 x 1 + 822
Step 2: Since the reminder 1144 ≠ 0, we apply division lemma to 822 and 1144, to get
1144 = 822 x 1 + 322
Step 3: We consider the new divisor 822 and the new remainder 322, and apply the division lemma to get
822 = 322 x 2 + 178
We consider the new divisor 322 and the new remainder 178,and apply the division lemma to get
322 = 178 x 1 + 144
We consider the new divisor 178 and the new remainder 144,and apply the division lemma to get
178 = 144 x 1 + 34
We consider the new divisor 144 and the new remainder 34,and apply the division lemma to get
144 = 34 x 4 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1144 and 1966 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(144,34) = HCF(178,144) = HCF(322,178) = HCF(822,322) = HCF(1144,822) = HCF(1966,1144) .
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 1144, 1966?
Answer: HCF of 1144, 1966 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1144, 1966 using Euclid's Algorithm?
Answer: For arbitrary numbers 1144, 1966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.