Highest Common Factor of 169, 524, 109 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 169, 524, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 169, 524, 109 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 169, 524, 109 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 169, 524, 109 is 1.
HCF(169, 524, 109) = 1
HCF of 169, 524, 109 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 169, 524, 109 is 1.
Highest Common Factor of 169,524,109 is 1
Step 1: Since 524 > 169, we apply the division lemma to 524 and 169, to get
524 = 169 x 3 + 17
Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 17 and 169, to get
169 = 17 x 9 + 16
Step 3: We consider the new divisor 17 and the new remainder 16, and apply the division lemma to get
17 = 16 x 1 + 1
We consider the new divisor 16 and the new remainder 1, and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 169 and 524 is 1
Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(169,17) = HCF(524,169) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 1, we apply the division lemma to 109 and 1, to get
109 = 1 x 109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 109 is 1
Notice that 1 = HCF(109,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 169, 524, 109 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 169, 524, 109?
Answer: HCF of 169, 524, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 169, 524, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 169, 524, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.