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 696, 2665, 1921 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 696, 2665, 1921 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 696, 2665, 1921 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 696, 2665, 1921 is 1.
HCF(696, 2665, 1921) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 696, 2665, 1921 is 1.
Step 1: Since 2665 > 696, we apply the division lemma to 2665 and 696, to get
2665 = 696 x 3 + 577
Step 2: Since the reminder 696 ≠ 0, we apply division lemma to 577 and 696, to get
696 = 577 x 1 + 119
Step 3: We consider the new divisor 577 and the new remainder 119, and apply the division lemma to get
577 = 119 x 4 + 101
We consider the new divisor 119 and the new remainder 101,and apply the division lemma to get
119 = 101 x 1 + 18
We consider the new divisor 101 and the new remainder 18,and apply the division lemma to get
101 = 18 x 5 + 11
We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get
18 = 11 x 1 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 696 and 2665 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(101,18) = HCF(119,101) = HCF(577,119) = HCF(696,577) = HCF(2665,696) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1921 > 1, we apply the division lemma to 1921 and 1, to get
1921 = 1 x 1921 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1921 is 1
Notice that 1 = HCF(1921,1) .
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 696, 2665, 1921?
Answer: HCF of 696, 2665, 1921 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 696, 2665, 1921 using Euclid's Algorithm?
Answer: For arbitrary numbers 696, 2665, 1921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.