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 312, 480, 775 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 480, 775 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 312, 480, 775 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 312, 480, 775 is 1.
HCF(312, 480, 775) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 480, 775 is 1.
Step 1: Since 480 > 312, we apply the division lemma to 480 and 312, to get
480 = 312 x 1 + 168
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 168 and 312, to get
312 = 168 x 1 + 144
Step 3: We consider the new divisor 168 and the new remainder 144, and apply the division lemma to get
168 = 144 x 1 + 24
We consider the new divisor 144 and the new remainder 24, and apply the division lemma to get
144 = 24 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 312 and 480 is 24
Notice that 24 = HCF(144,24) = HCF(168,144) = HCF(312,168) = HCF(480,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 775 > 24, we apply the division lemma to 775 and 24, to get
775 = 24 x 32 + 7
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 7 and 24, to get
24 = 7 x 3 + 3
Step 3: We consider the new divisor 7 and the new remainder 3, and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 24 and 775 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(775,24) .
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 312, 480, 775?
Answer: HCF of 312, 480, 775 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 480, 775 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 480, 775 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.