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, 861, 632, 10 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 509, 861, 632, 10 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, 861, 632, 10 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, 861, 632, 10 is 1.
HCF(509, 861, 632, 10) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 509, 861, 632, 10 is 1.
Step 1: Since 861 > 509, we apply the division lemma to 861 and 509, to get
861 = 509 x 1 + 352
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 352 and 509, to get
509 = 352 x 1 + 157
Step 3: We consider the new divisor 352 and the new remainder 157, and apply the division lemma to get
352 = 157 x 2 + 38
We consider the new divisor 157 and the new remainder 38,and apply the division lemma to get
157 = 38 x 4 + 5
We consider the new divisor 38 and the new remainder 5,and apply the division lemma to get
38 = 5 x 7 + 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 509 and 861 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(38,5) = HCF(157,38) = HCF(352,157) = HCF(509,352) = HCF(861,509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 632 > 1, we apply the division lemma to 632 and 1, to get
632 = 1 x 632 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 632 is 1
Notice that 1 = HCF(632,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 10 > 1, we apply the division lemma to 10 and 1, to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 10 is 1
Notice that 1 = HCF(10,1) .
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, 861, 632, 10?
Answer: HCF of 509, 861, 632, 10 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 509, 861, 632, 10 using Euclid's Algorithm?
Answer: For arbitrary numbers 509, 861, 632, 10 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.