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, 700, 728 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 700, 728 is 4 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, 700, 728 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, 700, 728 is 4.
HCF(460, 700, 728) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 700, 728 is 4.
Step 1: Since 700 > 460, we apply the division lemma to 700 and 460, to get
700 = 460 x 1 + 240
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 240 and 460, to get
460 = 240 x 1 + 220
Step 3: We consider the new divisor 240 and the new remainder 220, and apply the division lemma to get
240 = 220 x 1 + 20
We consider the new divisor 220 and the new remainder 20, and apply the division lemma to get
220 = 20 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 460 and 700 is 20
Notice that 20 = HCF(220,20) = HCF(240,220) = HCF(460,240) = HCF(700,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 728 > 20, we apply the division lemma to 728 and 20, to get
728 = 20 x 36 + 8
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 8 and 20, to get
20 = 8 x 2 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 728 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(728,20) .
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, 700, 728?
Answer: HCF of 460, 700, 728 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 700, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 700, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.