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 1767, 1578, 21559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1767, 1578, 21559 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 1767, 1578, 21559 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 1767, 1578, 21559 is 1.
HCF(1767, 1578, 21559) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1767, 1578, 21559 is 1.
Step 1: Since 1767 > 1578, we apply the division lemma to 1767 and 1578, to get
1767 = 1578 x 1 + 189
Step 2: Since the reminder 1578 ≠ 0, we apply division lemma to 189 and 1578, to get
1578 = 189 x 8 + 66
Step 3: We consider the new divisor 189 and the new remainder 66, and apply the division lemma to get
189 = 66 x 2 + 57
We consider the new divisor 66 and the new remainder 57,and apply the division lemma to get
66 = 57 x 1 + 9
We consider the new divisor 57 and the new remainder 9,and apply the division lemma to get
57 = 9 x 6 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1767 and 1578 is 3
Notice that 3 = HCF(9,3) = HCF(57,9) = HCF(66,57) = HCF(189,66) = HCF(1578,189) = HCF(1767,1578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21559 > 3, we apply the division lemma to 21559 and 3, to get
21559 = 3 x 7186 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 21559 is 1
Notice that 1 = HCF(3,1) = HCF(21559,3) .
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 1767, 1578, 21559?
Answer: HCF of 1767, 1578, 21559 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1767, 1578, 21559 using Euclid's Algorithm?
Answer: For arbitrary numbers 1767, 1578, 21559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.