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 752, 576, 352 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 752, 576, 352 is 16 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 752, 576, 352 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 752, 576, 352 is 16.
HCF(752, 576, 352) = 16
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 752, 576, 352 is 16.
Step 1: Since 752 > 576, we apply the division lemma to 752 and 576, to get
752 = 576 x 1 + 176
Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 176 and 576, to get
576 = 176 x 3 + 48
Step 3: We consider the new divisor 176 and the new remainder 48, and apply the division lemma to get
176 = 48 x 3 + 32
We consider the new divisor 48 and the new remainder 32,and apply the division lemma to get
48 = 32 x 1 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 752 and 576 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(176,48) = HCF(576,176) = HCF(752,576) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 352 > 16, we apply the division lemma to 352 and 16, to get
352 = 16 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 16 and 352 is 16
Notice that 16 = HCF(352,16) .
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 752, 576, 352?
Answer: HCF of 752, 576, 352 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 752, 576, 352 using Euclid's Algorithm?
Answer: For arbitrary numbers 752, 576, 352 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.