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 656, 519, 450 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 519, 450 is 1 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 656, 519, 450 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 656, 519, 450 is 1.
HCF(656, 519, 450) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 519, 450 is 1.
Step 1: Since 656 > 519, we apply the division lemma to 656 and 519, to get
656 = 519 x 1 + 137
Step 2: Since the reminder 519 ≠ 0, we apply division lemma to 137 and 519, to get
519 = 137 x 3 + 108
Step 3: We consider the new divisor 137 and the new remainder 108, and apply the division lemma to get
137 = 108 x 1 + 29
We consider the new divisor 108 and the new remainder 29,and apply the division lemma to get
108 = 29 x 3 + 21
We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get
29 = 21 x 1 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 656 and 519 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(108,29) = HCF(137,108) = HCF(519,137) = HCF(656,519) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 450 > 1, we apply the division lemma to 450 and 1, to get
450 = 1 x 450 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 450 is 1
Notice that 1 = HCF(450,1) .
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 656, 519, 450?
Answer: HCF of 656, 519, 450 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 519, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 519, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.