Highest Common Factor of 699, 997, 133 using Euclid's algorithm
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 699, 997, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 699, 997, 133 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 699, 997, 133 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 699, 997, 133 is 1.
HCF(699, 997, 133) = 1
HCF of 699, 997, 133 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 699, 997, 133 is 1.
Highest Common Factor of 699,997,133 is 1
Step 1: Since 997 > 699, we apply the division lemma to 997 and 699, to get
997 = 699 x 1 + 298
Step 2: Since the reminder 699 ≠ 0, we apply division lemma to 298 and 699, to get
699 = 298 x 2 + 103
Step 3: We consider the new divisor 298 and the new remainder 103, and apply the division lemma to get
298 = 103 x 2 + 92
We consider the new divisor 103 and the new remainder 92,and apply the division lemma to get
103 = 92 x 1 + 11
We consider the new divisor 92 and the new remainder 11,and apply the division lemma to get
92 = 11 x 8 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 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 699 and 997 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(92,11) = HCF(103,92) = HCF(298,103) = HCF(699,298) = HCF(997,699) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 133 > 1, we apply the division lemma to 133 and 1, to get
133 = 1 x 133 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 133 is 1
Notice that 1 = HCF(133,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 699, 997, 133 using Euclid's Algorithm
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 699, 997, 133?
Answer: HCF of 699, 997, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 699, 997, 133 using Euclid's Algorithm?
Answer: For arbitrary numbers 699, 997, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.