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 561, 297, 51 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 297, 51 is 3 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 561, 297, 51 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 561, 297, 51 is 3.
HCF(561, 297, 51) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 561, 297, 51 is 3.
Step 1: Since 561 > 297, we apply the division lemma to 561 and 297, to get
561 = 297 x 1 + 264
Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 264 and 297, to get
297 = 264 x 1 + 33
Step 3: We consider the new divisor 264 and the new remainder 33, and apply the division lemma to get
264 = 33 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 33, the HCF of 561 and 297 is 33
Notice that 33 = HCF(264,33) = HCF(297,264) = HCF(561,297) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 33, we apply the division lemma to 51 and 33, to get
51 = 33 x 1 + 18
Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 18 and 33, to get
33 = 18 x 1 + 15
Step 3: We consider the new divisor 18 and the new remainder 15, and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3, and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 33 and 51 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) .
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 561, 297, 51?
Answer: HCF of 561, 297, 51 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 297, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 297, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.