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 751, 3502, 9872 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 751, 3502, 9872 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 751, 3502, 9872 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 751, 3502, 9872 is 1.
HCF(751, 3502, 9872) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 751, 3502, 9872 is 1.
Step 1: Since 3502 > 751, we apply the division lemma to 3502 and 751, to get
3502 = 751 x 4 + 498
Step 2: Since the reminder 751 ≠ 0, we apply division lemma to 498 and 751, to get
751 = 498 x 1 + 253
Step 3: We consider the new divisor 498 and the new remainder 253, and apply the division lemma to get
498 = 253 x 1 + 245
We consider the new divisor 253 and the new remainder 245,and apply the division lemma to get
253 = 245 x 1 + 8
We consider the new divisor 245 and the new remainder 8,and apply the division lemma to get
245 = 8 x 30 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 751 and 3502 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(245,8) = HCF(253,245) = HCF(498,253) = HCF(751,498) = HCF(3502,751) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9872 > 1, we apply the division lemma to 9872 and 1, to get
9872 = 1 x 9872 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9872 is 1
Notice that 1 = HCF(9872,1) .
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 751, 3502, 9872?
Answer: HCF of 751, 3502, 9872 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 751, 3502, 9872 using Euclid's Algorithm?
Answer: For arbitrary numbers 751, 3502, 9872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.