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 262, 960, 784 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 262, 960, 784 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 262, 960, 784 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 262, 960, 784 is 2.
HCF(262, 960, 784) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 262, 960, 784 is 2.
Step 1: Since 960 > 262, we apply the division lemma to 960 and 262, to get
960 = 262 x 3 + 174
Step 2: Since the reminder 262 ≠ 0, we apply division lemma to 174 and 262, to get
262 = 174 x 1 + 88
Step 3: We consider the new divisor 174 and the new remainder 88, and apply the division lemma to get
174 = 88 x 1 + 86
We consider the new divisor 88 and the new remainder 86,and apply the division lemma to get
88 = 86 x 1 + 2
We consider the new divisor 86 and the new remainder 2,and apply the division lemma to get
86 = 2 x 43 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 262 and 960 is 2
Notice that 2 = HCF(86,2) = HCF(88,86) = HCF(174,88) = HCF(262,174) = HCF(960,262) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 784 > 2, we apply the division lemma to 784 and 2, to get
784 = 2 x 392 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 784 is 2
Notice that 2 = HCF(784,2) .
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 262, 960, 784?
Answer: HCF of 262, 960, 784 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 262, 960, 784 using Euclid's Algorithm?
Answer: For arbitrary numbers 262, 960, 784 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.