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 5056, 9208, 87898 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5056, 9208, 87898 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 5056, 9208, 87898 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 5056, 9208, 87898 is 2.
HCF(5056, 9208, 87898) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5056, 9208, 87898 is 2.
Step 1: Since 9208 > 5056, we apply the division lemma to 9208 and 5056, to get
9208 = 5056 x 1 + 4152
Step 2: Since the reminder 5056 ≠ 0, we apply division lemma to 4152 and 5056, to get
5056 = 4152 x 1 + 904
Step 3: We consider the new divisor 4152 and the new remainder 904, and apply the division lemma to get
4152 = 904 x 4 + 536
We consider the new divisor 904 and the new remainder 536,and apply the division lemma to get
904 = 536 x 1 + 368
We consider the new divisor 536 and the new remainder 368,and apply the division lemma to get
536 = 368 x 1 + 168
We consider the new divisor 368 and the new remainder 168,and apply the division lemma to get
368 = 168 x 2 + 32
We consider the new divisor 168 and the new remainder 32,and apply the division lemma to get
168 = 32 x 5 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 5056 and 9208 is 8
Notice that 8 = HCF(32,8) = HCF(168,32) = HCF(368,168) = HCF(536,368) = HCF(904,536) = HCF(4152,904) = HCF(5056,4152) = HCF(9208,5056) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 87898 > 8, we apply the division lemma to 87898 and 8, to get
87898 = 8 x 10987 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 87898 is 2
Notice that 2 = HCF(8,2) = HCF(87898,8) .
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 5056, 9208, 87898?
Answer: HCF of 5056, 9208, 87898 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5056, 9208, 87898 using Euclid's Algorithm?
Answer: For arbitrary numbers 5056, 9208, 87898 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.