Highest Common Factor of 660, 968, 976 using Euclid's algorithm
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 660, 968, 976 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 968, 976 is 4 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 660, 968, 976 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 660, 968, 976 is 4.
HCF(660, 968, 976) = 4
HCF of 660, 968, 976 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 968, 976 is 4.
Highest Common Factor of 660,968,976 is 4
Step 1: Since 968 > 660, we apply the division lemma to 968 and 660, to get
968 = 660 x 1 + 308
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 308 and 660, to get
660 = 308 x 2 + 44
Step 3: We consider the new divisor 308 and the new remainder 44, and apply the division lemma to get
308 = 44 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 44, the HCF of 660 and 968 is 44
Notice that 44 = HCF(308,44) = HCF(660,308) = HCF(968,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 976 > 44, we apply the division lemma to 976 and 44, to get
976 = 44 x 22 + 8
Step 2: Since the reminder 44 ≠ 0, we apply division lemma to 8 and 44, to get
44 = 8 x 5 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 44 and 976 is 4
Notice that 4 = HCF(8,4) = HCF(44,8) = HCF(976,44) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 660, 968, 976 using Euclid's Algorithm
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 660, 968, 976?
Answer: HCF of 660, 968, 976 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 968, 976 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 968, 976 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.