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 509, 860, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 509, 860, 705 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 509, 860, 705 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 509, 860, 705 is 1.
HCF(509, 860, 705) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 509, 860, 705 is 1.
Step 1: Since 860 > 509, we apply the division lemma to 860 and 509, to get
860 = 509 x 1 + 351
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 351 and 509, to get
509 = 351 x 1 + 158
Step 3: We consider the new divisor 351 and the new remainder 158, and apply the division lemma to get
351 = 158 x 2 + 35
We consider the new divisor 158 and the new remainder 35,and apply the division lemma to get
158 = 35 x 4 + 18
We consider the new divisor 35 and the new remainder 18,and apply the division lemma to get
35 = 18 x 1 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 509 and 860 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(35,18) = HCF(158,35) = HCF(351,158) = HCF(509,351) = HCF(860,509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 705 > 1, we apply the division lemma to 705 and 1, to get
705 = 1 x 705 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 705 is 1
Notice that 1 = HCF(705,1) .
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 509, 860, 705?
Answer: HCF of 509, 860, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 509, 860, 705 using Euclid's Algorithm?
Answer: For arbitrary numbers 509, 860, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.