Highest Common Factor of 750, 460 using Euclid's algorithm
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 750, 460 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 750, 460 is 10 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 750, 460 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 750, 460 is 10.
HCF(750, 460) = 10
HCF of 750, 460 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 750, 460 is 10.
Highest Common Factor of 750,460 is 10
Step 1: Since 750 > 460, we apply the division lemma to 750 and 460, to get
750 = 460 x 1 + 290
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 290 and 460, to get
460 = 290 x 1 + 170
Step 3: We consider the new divisor 290 and the new remainder 170, and apply the division lemma to get
290 = 170 x 1 + 120
We consider the new divisor 170 and the new remainder 120,and apply the division lemma to get
170 = 120 x 1 + 50
We consider the new divisor 120 and the new remainder 50,and apply the division lemma to get
120 = 50 x 2 + 20
We consider the new divisor 50 and the new remainder 20,and apply the division lemma to get
50 = 20 x 2 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 750 and 460 is 10
Notice that 10 = HCF(20,10) = HCF(50,20) = HCF(120,50) = HCF(170,120) = HCF(290,170) = HCF(460,290) = HCF(750,460) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 750, 460 using Euclid's Algorithm
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 750, 460?
Answer: HCF of 750, 460 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 750, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 750, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.