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 269, 978, 964 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 269, 978, 964 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 269, 978, 964 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 269, 978, 964 is 1.
HCF(269, 978, 964) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 269, 978, 964 is 1.
Step 1: Since 978 > 269, we apply the division lemma to 978 and 269, to get
978 = 269 x 3 + 171
Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 171 and 269, to get
269 = 171 x 1 + 98
Step 3: We consider the new divisor 171 and the new remainder 98, and apply the division lemma to get
171 = 98 x 1 + 73
We consider the new divisor 98 and the new remainder 73,and apply the division lemma to get
98 = 73 x 1 + 25
We consider the new divisor 73 and the new remainder 25,and apply the division lemma to get
73 = 25 x 2 + 23
We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get
25 = 23 x 1 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 269 and 978 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(73,25) = HCF(98,73) = HCF(171,98) = HCF(269,171) = HCF(978,269) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 964 > 1, we apply the division lemma to 964 and 1, to get
964 = 1 x 964 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 964 is 1
Notice that 1 = HCF(964,1) .
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 269, 978, 964?
Answer: HCF of 269, 978, 964 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 269, 978, 964 using Euclid's Algorithm?
Answer: For arbitrary numbers 269, 978, 964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.