Highest Common Factor of 32, 21, 38 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 32, 21, 38 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 32, 21, 38 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 32, 21, 38 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 32, 21, 38 is 1.
HCF(32, 21, 38) = 1
HCF of 32, 21, 38 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 32, 21, 38 is 1.
Highest Common Factor of 32,21,38 is 1
Step 1: Since 32 > 21, we apply the division lemma to 32 and 21, to get
32 = 21 x 1 + 11
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 11 and 21, to get
21 = 11 x 1 + 10
Step 3: We consider the new divisor 11 and the new remainder 10, and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1, and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 32 and 21 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 1, we apply the division lemma to 38 and 1, to get
38 = 1 x 38 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 38 is 1
Notice that 1 = HCF(38,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 32, 21, 38 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 32, 21, 38?
Answer: HCF of 32, 21, 38 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 32, 21, 38 using Euclid's Algorithm?
Answer: For arbitrary numbers 32, 21, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.