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 849, 669, 832 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 849, 669, 832 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 849, 669, 832 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 849, 669, 832 is 1.
HCF(849, 669, 832) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 849, 669, 832 is 1.
Step 1: Since 849 > 669, we apply the division lemma to 849 and 669, to get
849 = 669 x 1 + 180
Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 180 and 669, to get
669 = 180 x 3 + 129
Step 3: We consider the new divisor 180 and the new remainder 129, and apply the division lemma to get
180 = 129 x 1 + 51
We consider the new divisor 129 and the new remainder 51,and apply the division lemma to get
129 = 51 x 2 + 27
We consider the new divisor 51 and the new remainder 27,and apply the division lemma to get
51 = 27 x 1 + 24
We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get
27 = 24 x 1 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 849 and 669 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(51,27) = HCF(129,51) = HCF(180,129) = HCF(669,180) = HCF(849,669) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 832 > 3, we apply the division lemma to 832 and 3, to get
832 = 3 x 277 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 832 is 1
Notice that 1 = HCF(3,1) = HCF(832,3) .
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 849, 669, 832?
Answer: HCF of 849, 669, 832 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 849, 669, 832 using Euclid's Algorithm?
Answer: For arbitrary numbers 849, 669, 832 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.