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 256, 994, 997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 256, 994, 997 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 256, 994, 997 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 256, 994, 997 is 1.
HCF(256, 994, 997) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 256, 994, 997 is 1.
Step 1: Since 994 > 256, we apply the division lemma to 994 and 256, to get
994 = 256 x 3 + 226
Step 2: Since the reminder 256 ≠ 0, we apply division lemma to 226 and 256, to get
256 = 226 x 1 + 30
Step 3: We consider the new divisor 226 and the new remainder 30, and apply the division lemma to get
226 = 30 x 7 + 16
We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get
30 = 16 x 1 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 256 and 994 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(226,30) = HCF(256,226) = HCF(994,256) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 997 > 2, we apply the division lemma to 997 and 2, to get
997 = 2 x 498 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 997 is 1
Notice that 1 = HCF(2,1) = HCF(997,2) .
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 256, 994, 997?
Answer: HCF of 256, 994, 997 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 256, 994, 997 using Euclid's Algorithm?
Answer: For arbitrary numbers 256, 994, 997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.