Highest Common Factor of 154, 262, 65 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 154, 262, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 154, 262, 65 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 154, 262, 65 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 154, 262, 65 is 1.
HCF(154, 262, 65) = 1
HCF of 154, 262, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 154, 262, 65 is 1.
Highest Common Factor of 154,262,65 is 1
Step 1: Since 262 > 154, we apply the division lemma to 262 and 154, to get
262 = 154 x 1 + 108
Step 2: Since the reminder 154 ≠ 0, we apply division lemma to 108 and 154, to get
154 = 108 x 1 + 46
Step 3: We consider the new divisor 108 and the new remainder 46, and apply the division lemma to get
108 = 46 x 2 + 16
We consider the new divisor 46 and the new remainder 16,and apply the division lemma to get
46 = 16 x 2 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 154 and 262 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(46,16) = HCF(108,46) = HCF(154,108) = HCF(262,154) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 2, we apply the division lemma to 65 and 2, to get
65 = 2 x 32 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 65 is 1
Notice that 1 = HCF(2,1) = HCF(65,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 154, 262, 65 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 154, 262, 65?
Answer: HCF of 154, 262, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 154, 262, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 154, 262, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.