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 297, 968, 132 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 297, 968, 132 is 11 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 297, 968, 132 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 297, 968, 132 is 11.
HCF(297, 968, 132) = 11
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 297, 968, 132 is 11.
Step 1: Since 968 > 297, we apply the division lemma to 968 and 297, to get
968 = 297 x 3 + 77
Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 77 and 297, to get
297 = 77 x 3 + 66
Step 3: We consider the new divisor 77 and the new remainder 66, and apply the division lemma to get
77 = 66 x 1 + 11
We consider the new divisor 66 and the new remainder 11, and apply the division lemma to get
66 = 11 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 297 and 968 is 11
Notice that 11 = HCF(66,11) = HCF(77,66) = HCF(297,77) = HCF(968,297) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 132 > 11, we apply the division lemma to 132 and 11, to get
132 = 11 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 11 and 132 is 11
Notice that 11 = HCF(132,11) .
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 297, 968, 132?
Answer: HCF of 297, 968, 132 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 297, 968, 132 using Euclid's Algorithm?
Answer: For arbitrary numbers 297, 968, 132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.