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 87, 319, 569 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 87, 319, 569 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 87, 319, 569 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 87, 319, 569 is 1.
HCF(87, 319, 569) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 87, 319, 569 is 1.
Step 1: Since 319 > 87, we apply the division lemma to 319 and 87, to get
319 = 87 x 3 + 58
Step 2: Since the reminder 87 ≠ 0, we apply division lemma to 58 and 87, to get
87 = 58 x 1 + 29
Step 3: We consider the new divisor 58 and the new remainder 29, and apply the division lemma to get
58 = 29 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 87 and 319 is 29
Notice that 29 = HCF(58,29) = HCF(87,58) = HCF(319,87) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 569 > 29, we apply the division lemma to 569 and 29, to get
569 = 29 x 19 + 18
Step 2: Since the reminder 29 ≠ 0, we apply division lemma to 18 and 29, to get
29 = 18 x 1 + 11
Step 3: We consider the new divisor 18 and the new remainder 11, and apply the division lemma to get
18 = 11 x 1 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 29 and 569 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(29,18) = HCF(569,29) .
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 87, 319, 569?
Answer: HCF of 87, 319, 569 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 87, 319, 569 using Euclid's Algorithm?
Answer: For arbitrary numbers 87, 319, 569 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.