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 456, 268, 671 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 456, 268, 671 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 456, 268, 671 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 456, 268, 671 is 1.
HCF(456, 268, 671) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 456, 268, 671 is 1.
Step 1: Since 456 > 268, we apply the division lemma to 456 and 268, to get
456 = 268 x 1 + 188
Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 188 and 268, to get
268 = 188 x 1 + 80
Step 3: We consider the new divisor 188 and the new remainder 80, and apply the division lemma to get
188 = 80 x 2 + 28
We consider the new divisor 80 and the new remainder 28,and apply the division lemma to get
80 = 28 x 2 + 24
We consider the new divisor 28 and the new remainder 24,and apply the division lemma to get
28 = 24 x 1 + 4
We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get
24 = 4 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 456 and 268 is 4
Notice that 4 = HCF(24,4) = HCF(28,24) = HCF(80,28) = HCF(188,80) = HCF(268,188) = HCF(456,268) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 671 > 4, we apply the division lemma to 671 and 4, to get
671 = 4 x 167 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 671 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(671,4) .
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 456, 268, 671?
Answer: HCF of 456, 268, 671 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 456, 268, 671 using Euclid's Algorithm?
Answer: For arbitrary numbers 456, 268, 671 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.