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 855, 675, 885 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 855, 675, 885 is 15 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 855, 675, 885 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 855, 675, 885 is 15.
HCF(855, 675, 885) = 15
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 855, 675, 885 is 15.
Step 1: Since 855 > 675, we apply the division lemma to 855 and 675, to get
855 = 675 x 1 + 180
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 180 and 675, to get
675 = 180 x 3 + 135
Step 3: We consider the new divisor 180 and the new remainder 135, and apply the division lemma to get
180 = 135 x 1 + 45
We consider the new divisor 135 and the new remainder 45, and apply the division lemma to get
135 = 45 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 855 and 675 is 45
Notice that 45 = HCF(135,45) = HCF(180,135) = HCF(675,180) = HCF(855,675) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 885 > 45, we apply the division lemma to 885 and 45, to get
885 = 45 x 19 + 30
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 30 and 45, to get
45 = 30 x 1 + 15
Step 3: We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 45 and 885 is 15
Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(885,45) .
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 855, 675, 885?
Answer: HCF of 855, 675, 885 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 855, 675, 885 using Euclid's Algorithm?
Answer: For arbitrary numbers 855, 675, 885 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.