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, 517, 751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 517, 751 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, 517, 751 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, 517, 751 is 1.
HCF(312, 517, 751) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 517, 751 is 1.
Step 1: Since 517 > 312, we apply the division lemma to 517 and 312, to get
517 = 312 x 1 + 205
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 205 and 312, to get
312 = 205 x 1 + 107
Step 3: We consider the new divisor 205 and the new remainder 107, and apply the division lemma to get
205 = 107 x 1 + 98
We consider the new divisor 107 and the new remainder 98,and apply the division lemma to get
107 = 98 x 1 + 9
We consider the new divisor 98 and the new remainder 9,and apply the division lemma to get
98 = 9 x 10 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 312 and 517 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(98,9) = HCF(107,98) = HCF(205,107) = HCF(312,205) = HCF(517,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 751 > 1, we apply the division lemma to 751 and 1, to get
751 = 1 x 751 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 751 is 1
Notice that 1 = HCF(751,1) .
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, 517, 751?
Answer: HCF of 312, 517, 751 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 517, 751 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 517, 751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.