Highest Common Factor of 48, 128, 338 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 48, 128, 338 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 48, 128, 338 is 2 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 48, 128, 338 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 48, 128, 338 is 2.
HCF(48, 128, 338) = 2
HCF of 48, 128, 338 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 48, 128, 338 is 2.
Highest Common Factor of 48,128,338 is 2
Step 1: Since 128 > 48, we apply the division lemma to 128 and 48, to get
128 = 48 x 2 + 32
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 32 and 48, to get
48 = 32 x 1 + 16
Step 3: We consider the new divisor 32 and the new remainder 16, and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 48 and 128 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(128,48) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 338 > 16, we apply the division lemma to 338 and 16, to get
338 = 16 x 21 + 2
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 2 and 16, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 338 is 2
Notice that 2 = HCF(16,2) = HCF(338,16) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 48, 128, 338 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 48, 128, 338?
Answer: HCF of 48, 128, 338 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 48, 128, 338 using Euclid's Algorithm?
Answer: For arbitrary numbers 48, 128, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.