Highest Common Factor of 137, 321, 168 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 137, 321, 168 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 137, 321, 168 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 137, 321, 168 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 137, 321, 168 is 1.
HCF(137, 321, 168) = 1
HCF of 137, 321, 168 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 137, 321, 168 is 1.
Highest Common Factor of 137,321,168 is 1
Step 1: Since 321 > 137, we apply the division lemma to 321 and 137, to get
321 = 137 x 2 + 47
Step 2: Since the reminder 137 ≠ 0, we apply division lemma to 47 and 137, to get
137 = 47 x 2 + 43
Step 3: We consider the new divisor 47 and the new remainder 43, and apply the division lemma to get
47 = 43 x 1 + 4
We consider the new divisor 43 and the new remainder 4,and apply the division lemma to get
43 = 4 x 10 + 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 137 and 321 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(43,4) = HCF(47,43) = HCF(137,47) = HCF(321,137) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 168 > 1, we apply the division lemma to 168 and 1, to get
168 = 1 x 168 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 168 is 1
Notice that 1 = HCF(168,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 137, 321, 168 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 137, 321, 168?
Answer: HCF of 137, 321, 168 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 137, 321, 168 using Euclid's Algorithm?
Answer: For arbitrary numbers 137, 321, 168 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.