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 517, 921, 992 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 517, 921, 992 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 517, 921, 992 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 517, 921, 992 is 1.
HCF(517, 921, 992) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 517, 921, 992 is 1.
Step 1: Since 921 > 517, we apply the division lemma to 921 and 517, to get
921 = 517 x 1 + 404
Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 404 and 517, to get
517 = 404 x 1 + 113
Step 3: We consider the new divisor 404 and the new remainder 113, and apply the division lemma to get
404 = 113 x 3 + 65
We consider the new divisor 113 and the new remainder 65,and apply the division lemma to get
113 = 65 x 1 + 48
We consider the new divisor 65 and the new remainder 48,and apply the division lemma to get
65 = 48 x 1 + 17
We consider the new divisor 48 and the new remainder 17,and apply the division lemma to get
48 = 17 x 2 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 517 and 921 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(48,17) = HCF(65,48) = HCF(113,65) = HCF(404,113) = HCF(517,404) = HCF(921,517) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 992 > 1, we apply the division lemma to 992 and 1, to get
992 = 1 x 992 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 992 is 1
Notice that 1 = HCF(992,1) .
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 517, 921, 992?
Answer: HCF of 517, 921, 992 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 517, 921, 992 using Euclid's Algorithm?
Answer: For arbitrary numbers 517, 921, 992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.