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 330, 602, 560 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 330, 602, 560 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 330, 602, 560 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 330, 602, 560 is 2.
HCF(330, 602, 560) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 330, 602, 560 is 2.
Step 1: Since 602 > 330, we apply the division lemma to 602 and 330, to get
602 = 330 x 1 + 272
Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 272 and 330, to get
330 = 272 x 1 + 58
Step 3: We consider the new divisor 272 and the new remainder 58, and apply the division lemma to get
272 = 58 x 4 + 40
We consider the new divisor 58 and the new remainder 40,and apply the division lemma to get
58 = 40 x 1 + 18
We consider the new divisor 40 and the new remainder 18,and apply the division lemma to get
40 = 18 x 2 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 330 and 602 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(40,18) = HCF(58,40) = HCF(272,58) = HCF(330,272) = HCF(602,330) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 560 > 2, we apply the division lemma to 560 and 2, to get
560 = 2 x 280 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 560 is 2
Notice that 2 = HCF(560,2) .
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 330, 602, 560?
Answer: HCF of 330, 602, 560 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 330, 602, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 330, 602, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.