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 876, 578, 988 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 876, 578, 988 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 876, 578, 988 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 876, 578, 988 is 2.
HCF(876, 578, 988) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 876, 578, 988 is 2.
Step 1: Since 876 > 578, we apply the division lemma to 876 and 578, to get
876 = 578 x 1 + 298
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 298 and 578, to get
578 = 298 x 1 + 280
Step 3: We consider the new divisor 298 and the new remainder 280, and apply the division lemma to get
298 = 280 x 1 + 18
We consider the new divisor 280 and the new remainder 18,and apply the division lemma to get
280 = 18 x 15 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma 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 876 and 578 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(280,18) = HCF(298,280) = HCF(578,298) = HCF(876,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 988 > 2, we apply the division lemma to 988 and 2, to get
988 = 2 x 494 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 988 is 2
Notice that 2 = HCF(988,2) .
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 876, 578, 988?
Answer: HCF of 876, 578, 988 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 876, 578, 988 using Euclid's Algorithm?
Answer: For arbitrary numbers 876, 578, 988 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.