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 320, 244, 60 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 320, 244, 60 is 4 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 320, 244, 60 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 320, 244, 60 is 4.
HCF(320, 244, 60) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 320, 244, 60 is 4.
Step 1: Since 320 > 244, we apply the division lemma to 320 and 244, to get
320 = 244 x 1 + 76
Step 2: Since the reminder 244 ≠ 0, we apply division lemma to 76 and 244, to get
244 = 76 x 3 + 16
Step 3: We consider the new divisor 76 and the new remainder 16, and apply the division lemma to get
76 = 16 x 4 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 320 and 244 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(76,16) = HCF(244,76) = HCF(320,244) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 4, we apply the division lemma to 60 and 4, to get
60 = 4 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 60 is 4
Notice that 4 = HCF(60,4) .
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 320, 244, 60?
Answer: HCF of 320, 244, 60 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 320, 244, 60 using Euclid's Algorithm?
Answer: For arbitrary numbers 320, 244, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.