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 345, 440, 45 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 440, 45 is 5 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 345, 440, 45 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 345, 440, 45 is 5.
HCF(345, 440, 45) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 440, 45 is 5.
Step 1: Since 440 > 345, we apply the division lemma to 440 and 345, to get
440 = 345 x 1 + 95
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 95 and 345, to get
345 = 95 x 3 + 60
Step 3: We consider the new divisor 95 and the new remainder 60, and apply the division lemma to get
95 = 60 x 1 + 35
We consider the new divisor 60 and the new remainder 35,and apply the division lemma to get
60 = 35 x 1 + 25
We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get
35 = 25 x 1 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 345 and 440 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(60,35) = HCF(95,60) = HCF(345,95) = HCF(440,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 5, we apply the division lemma to 45 and 5, to get
45 = 5 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 45 is 5
Notice that 5 = HCF(45,5) .
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 345, 440, 45?
Answer: HCF of 345, 440, 45 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 440, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 440, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.