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 990, 625, 110 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 625, 110 is 5 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 990, 625, 110 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 990, 625, 110 is 5.
HCF(990, 625, 110) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 990, 625, 110 is 5.
Step 1: Since 990 > 625, we apply the division lemma to 990 and 625, to get
990 = 625 x 1 + 365
Step 2: Since the reminder 625 ≠ 0, we apply division lemma to 365 and 625, to get
625 = 365 x 1 + 260
Step 3: We consider the new divisor 365 and the new remainder 260, and apply the division lemma to get
365 = 260 x 1 + 105
We consider the new divisor 260 and the new remainder 105,and apply the division lemma to get
260 = 105 x 2 + 50
We consider the new divisor 105 and the new remainder 50,and apply the division lemma to get
105 = 50 x 2 + 5
We consider the new divisor 50 and the new remainder 5,and apply the division lemma to get
50 = 5 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 990 and 625 is 5
Notice that 5 = HCF(50,5) = HCF(105,50) = HCF(260,105) = HCF(365,260) = HCF(625,365) = HCF(990,625) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 110 > 5, we apply the division lemma to 110 and 5, to get
110 = 5 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 110 is 5
Notice that 5 = HCF(110,5) .
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 990, 625, 110?
Answer: HCF of 990, 625, 110 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 625, 110 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 625, 110 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.