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, 353, 144 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 456, 353, 144 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, 353, 144 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, 353, 144 is 1.
HCF(456, 353, 144) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 456, 353, 144 is 1.
Step 1: Since 456 > 353, we apply the division lemma to 456 and 353, to get
456 = 353 x 1 + 103
Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 103 and 353, to get
353 = 103 x 3 + 44
Step 3: We consider the new divisor 103 and the new remainder 44, and apply the division lemma to get
103 = 44 x 2 + 15
We consider the new divisor 44 and the new remainder 15,and apply the division lemma to get
44 = 15 x 2 + 14
We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get
15 = 14 x 1 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 456 and 353 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(44,15) = HCF(103,44) = HCF(353,103) = HCF(456,353) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 144 > 1, we apply the division lemma to 144 and 1, to get
144 = 1 x 144 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 144 is 1
Notice that 1 = HCF(144,1) .
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 456, 353, 144?
Answer: HCF of 456, 353, 144 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 456, 353, 144 using Euclid's Algorithm?
Answer: For arbitrary numbers 456, 353, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.