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 40, 880, 654 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 40, 880, 654 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 40, 880, 654 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 40, 880, 654 is 2.
HCF(40, 880, 654) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 40, 880, 654 is 2.
Step 1: Since 880 > 40, we apply the division lemma to 880 and 40, to get
880 = 40 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 40 and 880 is 40
Notice that 40 = HCF(880,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 654 > 40, we apply the division lemma to 654 and 40, to get
654 = 40 x 16 + 14
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 14 and 40, to get
40 = 14 x 2 + 12
Step 3: We consider the new divisor 14 and the new remainder 12, and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2, and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 40 and 654 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(40,14) = HCF(654,40) .
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 40, 880, 654?
Answer: HCF of 40, 880, 654 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 40, 880, 654 using Euclid's Algorithm?
Answer: For arbitrary numbers 40, 880, 654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.