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 408, 720, 26 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 720, 26 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 408, 720, 26 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 408, 720, 26 is 2.
HCF(408, 720, 26) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 720, 26 is 2.
Step 1: Since 720 > 408, we apply the division lemma to 720 and 408, to get
720 = 408 x 1 + 312
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 312 and 408, to get
408 = 312 x 1 + 96
Step 3: We consider the new divisor 312 and the new remainder 96, and apply the division lemma to get
312 = 96 x 3 + 24
We consider the new divisor 96 and the new remainder 24, and apply the division lemma to get
96 = 24 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 408 and 720 is 24
Notice that 24 = HCF(96,24) = HCF(312,96) = HCF(408,312) = HCF(720,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 26 > 24, we apply the division lemma to 26 and 24, to get
26 = 24 x 1 + 2
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 2 and 24, to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 24 and 26 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) .
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 408, 720, 26?
Answer: HCF of 408, 720, 26 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 720, 26 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 720, 26 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.