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 880, 6540, 3990 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 880, 6540, 3990 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 880, 6540, 3990 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 880, 6540, 3990 is 10.
HCF(880, 6540, 3990) = 10
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 880, 6540, 3990 is 10.
Step 1: Since 6540 > 880, we apply the division lemma to 6540 and 880, to get
6540 = 880 x 7 + 380
Step 2: Since the reminder 880 ≠ 0, we apply division lemma to 380 and 880, to get
880 = 380 x 2 + 120
Step 3: We consider the new divisor 380 and the new remainder 120, and apply the division lemma to get
380 = 120 x 3 + 20
We consider the new divisor 120 and the new remainder 20, and apply the division lemma to get
120 = 20 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 880 and 6540 is 20
Notice that 20 = HCF(120,20) = HCF(380,120) = HCF(880,380) = HCF(6540,880) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3990 > 20, we apply the division lemma to 3990 and 20, to get
3990 = 20 x 199 + 10
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 10 and 20, 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 20 and 3990 is 10
Notice that 10 = HCF(20,10) = HCF(3990,20) .
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 880, 6540, 3990?
Answer: HCF of 880, 6540, 3990 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 880, 6540, 3990 using Euclid's Algorithm?
Answer: For arbitrary numbers 880, 6540, 3990 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.