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, 650, 158 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 169, 650, 158 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, 650, 158 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, 650, 158 is 1.
HCF(169, 650, 158) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 169, 650, 158 is 1.
Step 1: Since 650 > 169, we apply the division lemma to 650 and 169, to get
650 = 169 x 3 + 143
Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 143 and 169, to get
169 = 143 x 1 + 26
Step 3: We consider the new divisor 143 and the new remainder 26, and apply the division lemma to get
143 = 26 x 5 + 13
We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get
26 = 13 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 169 and 650 is 13
Notice that 13 = HCF(26,13) = HCF(143,26) = HCF(169,143) = HCF(650,169) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 158 > 13, we apply the division lemma to 158 and 13, to get
158 = 13 x 12 + 2
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 2 and 13, to get
13 = 2 x 6 + 1
Step 3: 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 13 and 158 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(158,13) .
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 169, 650, 158?
Answer: HCF of 169, 650, 158 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 169, 650, 158 using Euclid's Algorithm?
Answer: For arbitrary numbers 169, 650, 158 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.