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 161, 699, 814, 57 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 161, 699, 814, 57 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 161, 699, 814, 57 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 161, 699, 814, 57 is 1.
HCF(161, 699, 814, 57) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 161, 699, 814, 57 is 1.
Step 1: Since 699 > 161, we apply the division lemma to 699 and 161, to get
699 = 161 x 4 + 55
Step 2: Since the reminder 161 ≠ 0, we apply division lemma to 55 and 161, to get
161 = 55 x 2 + 51
Step 3: We consider the new divisor 55 and the new remainder 51, and apply the division lemma to get
55 = 51 x 1 + 4
We consider the new divisor 51 and the new remainder 4,and apply the division lemma to get
51 = 4 x 12 + 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 161 and 699 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(51,4) = HCF(55,51) = HCF(161,55) = HCF(699,161) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 1, we apply the division lemma to 814 and 1, to get
814 = 1 x 814 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 814 is 1
Notice that 1 = HCF(814,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57 > 1, we apply the division lemma to 57 and 1, to get
57 = 1 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 57 is 1
Notice that 1 = HCF(57,1) .
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 161, 699, 814, 57?
Answer: HCF of 161, 699, 814, 57 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 161, 699, 814, 57 using Euclid's Algorithm?
Answer: For arbitrary numbers 161, 699, 814, 57 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.