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 460, 745, 247 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 745, 247 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 460, 745, 247 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 460, 745, 247 is 1.
HCF(460, 745, 247) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 745, 247 is 1.
Step 1: Since 745 > 460, we apply the division lemma to 745 and 460, to get
745 = 460 x 1 + 285
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 285 and 460, to get
460 = 285 x 1 + 175
Step 3: We consider the new divisor 285 and the new remainder 175, and apply the division lemma to get
285 = 175 x 1 + 110
We consider the new divisor 175 and the new remainder 110,and apply the division lemma to get
175 = 110 x 1 + 65
We consider the new divisor 110 and the new remainder 65,and apply the division lemma to get
110 = 65 x 1 + 45
We consider the new divisor 65 and the new remainder 45,and apply the division lemma to get
65 = 45 x 1 + 20
We consider the new divisor 45 and the new remainder 20,and apply the division lemma to get
45 = 20 x 2 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 460 and 745 is 5
Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(65,45) = HCF(110,65) = HCF(175,110) = HCF(285,175) = HCF(460,285) = HCF(745,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 247 > 5, we apply the division lemma to 247 and 5, to get
247 = 5 x 49 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 247 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(247,5) .
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 460, 745, 247?
Answer: HCF of 460, 745, 247 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 745, 247 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 745, 247 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.