Highest Common Factor of 661, 968, 119 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 661, 968, 119 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 968, 119 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 661, 968, 119 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 661, 968, 119 is 1.
HCF(661, 968, 119) = 1
HCF of 661, 968, 119 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 661, 968, 119 is 1.
Highest Common Factor of 661,968,119 is 1
Step 1: Since 968 > 661, we apply the division lemma to 968 and 661, to get
968 = 661 x 1 + 307
Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 307 and 661, to get
661 = 307 x 2 + 47
Step 3: We consider the new divisor 307 and the new remainder 47, and apply the division lemma to get
307 = 47 x 6 + 25
We consider the new divisor 47 and the new remainder 25,and apply the division lemma to get
47 = 25 x 1 + 22
We consider the new divisor 25 and the new remainder 22,and apply the division lemma to get
25 = 22 x 1 + 3
We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get
22 = 3 x 7 + 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 661 and 968 is 1
Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(25,22) = HCF(47,25) = HCF(307,47) = HCF(661,307) = HCF(968,661) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 119 > 1, we apply the division lemma to 119 and 1, to get
119 = 1 x 119 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 119 is 1
Notice that 1 = HCF(119,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 661, 968, 119 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 661, 968, 119?
Answer: HCF of 661, 968, 119 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 968, 119 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 968, 119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.