Highest Common Factor of 352, 610, 288 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 352, 610, 288 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 352, 610, 288 is 2 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 352, 610, 288 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 352, 610, 288 is 2.
HCF(352, 610, 288) = 2
HCF of 352, 610, 288 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 352, 610, 288 is 2.
Highest Common Factor of 352,610,288 is 2
Step 1: Since 610 > 352, we apply the division lemma to 610 and 352, to get
610 = 352 x 1 + 258
Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 258 and 352, to get
352 = 258 x 1 + 94
Step 3: We consider the new divisor 258 and the new remainder 94, and apply the division lemma to get
258 = 94 x 2 + 70
We consider the new divisor 94 and the new remainder 70,and apply the division lemma to get
94 = 70 x 1 + 24
We consider the new divisor 70 and the new remainder 24,and apply the division lemma to get
70 = 24 x 2 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 352 and 610 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(70,24) = HCF(94,70) = HCF(258,94) = HCF(352,258) = HCF(610,352) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 288 > 2, we apply the division lemma to 288 and 2, to get
288 = 2 x 144 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 288 is 2
Notice that 2 = HCF(288,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 352, 610, 288 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 352, 610, 288?
Answer: HCF of 352, 610, 288 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 352, 610, 288 using Euclid's Algorithm?
Answer: For arbitrary numbers 352, 610, 288 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.