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 38, 78, 54, 320 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 38, 78, 54, 320 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 38, 78, 54, 320 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 38, 78, 54, 320 is 2.
HCF(38, 78, 54, 320) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 38, 78, 54, 320 is 2.
Step 1: Since 78 > 38, we apply the division lemma to 78 and 38, to get
78 = 38 x 2 + 2
Step 2: Since the reminder 38 ≠ 0, we apply division lemma to 2 and 38, to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 38 and 78 is 2
Notice that 2 = HCF(38,2) = HCF(78,38) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 2, we apply the division lemma to 54 and 2, to get
54 = 2 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 54 is 2
Notice that 2 = HCF(54,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 320 > 2, we apply the division lemma to 320 and 2, to get
320 = 2 x 160 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 320 is 2
Notice that 2 = HCF(320,2) .
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 38, 78, 54, 320?
Answer: HCF of 38, 78, 54, 320 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 38, 78, 54, 320 using Euclid's Algorithm?
Answer: For arbitrary numbers 38, 78, 54, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.