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 720, 410, 145 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 410, 145 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 720, 410, 145 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 720, 410, 145 is 5.
HCF(720, 410, 145) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 410, 145 is 5.
Step 1: Since 720 > 410, we apply the division lemma to 720 and 410, to get
720 = 410 x 1 + 310
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 310 and 410, to get
410 = 310 x 1 + 100
Step 3: We consider the new divisor 310 and the new remainder 100, and apply the division lemma to get
310 = 100 x 3 + 10
We consider the new divisor 100 and the new remainder 10, and apply the division lemma to get
100 = 10 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 720 and 410 is 10
Notice that 10 = HCF(100,10) = HCF(310,100) = HCF(410,310) = HCF(720,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 145 > 10, we apply the division lemma to 145 and 10, to get
145 = 10 x 14 + 5
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 5 and 10, 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 10 and 145 is 5
Notice that 5 = HCF(10,5) = HCF(145,10) .
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 720, 410, 145?
Answer: HCF of 720, 410, 145 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 410, 145 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 410, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.