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 817, 560, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 817, 560, 421 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 817, 560, 421 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 817, 560, 421 is 1.
HCF(817, 560, 421) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 817, 560, 421 is 1.
Step 1: Since 817 > 560, we apply the division lemma to 817 and 560, to get
817 = 560 x 1 + 257
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 257 and 560, to get
560 = 257 x 2 + 46
Step 3: We consider the new divisor 257 and the new remainder 46, and apply the division lemma to get
257 = 46 x 5 + 27
We consider the new divisor 46 and the new remainder 27,and apply the division lemma to get
46 = 27 x 1 + 19
We consider the new divisor 27 and the new remainder 19,and apply the division lemma to get
27 = 19 x 1 + 8
We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get
19 = 8 x 2 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 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 817 and 560 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(46,27) = HCF(257,46) = HCF(560,257) = HCF(817,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 421 > 1, we apply the division lemma to 421 and 1, to get
421 = 1 x 421 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 421 is 1
Notice that 1 = HCF(421,1) .
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 817, 560, 421?
Answer: HCF of 817, 560, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 817, 560, 421 using Euclid's Algorithm?
Answer: For arbitrary numbers 817, 560, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.