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 999, 580, 949 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 999, 580, 949 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 999, 580, 949 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 999, 580, 949 is 1.
HCF(999, 580, 949) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 999, 580, 949 is 1.
Step 1: Since 999 > 580, we apply the division lemma to 999 and 580, to get
999 = 580 x 1 + 419
Step 2: Since the reminder 580 ≠ 0, we apply division lemma to 419 and 580, to get
580 = 419 x 1 + 161
Step 3: We consider the new divisor 419 and the new remainder 161, and apply the division lemma to get
419 = 161 x 2 + 97
We consider the new divisor 161 and the new remainder 97,and apply the division lemma to get
161 = 97 x 1 + 64
We consider the new divisor 97 and the new remainder 64,and apply the division lemma to get
97 = 64 x 1 + 33
We consider the new divisor 64 and the new remainder 33,and apply the division lemma to get
64 = 33 x 1 + 31
We consider the new divisor 33 and the new remainder 31,and apply the division lemma to get
33 = 31 x 1 + 2
We consider the new divisor 31 and the new remainder 2,and apply the division lemma to get
31 = 2 x 15 + 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 999 and 580 is 1
Notice that 1 = HCF(2,1) = HCF(31,2) = HCF(33,31) = HCF(64,33) = HCF(97,64) = HCF(161,97) = HCF(419,161) = HCF(580,419) = HCF(999,580) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 949 > 1, we apply the division lemma to 949 and 1, to get
949 = 1 x 949 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 949 is 1
Notice that 1 = HCF(949,1) .
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 999, 580, 949?
Answer: HCF of 999, 580, 949 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 999, 580, 949 using Euclid's Algorithm?
Answer: For arbitrary numbers 999, 580, 949 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.