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 852, 315, 354 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 852, 315, 354 is 3 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 852, 315, 354 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 852, 315, 354 is 3.
HCF(852, 315, 354) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 852, 315, 354 is 3.
Step 1: Since 852 > 315, we apply the division lemma to 852 and 315, to get
852 = 315 x 2 + 222
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 222 and 315, to get
315 = 222 x 1 + 93
Step 3: We consider the new divisor 222 and the new remainder 93, and apply the division lemma to get
222 = 93 x 2 + 36
We consider the new divisor 93 and the new remainder 36,and apply the division lemma to get
93 = 36 x 2 + 21
We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 852 and 315 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(93,36) = HCF(222,93) = HCF(315,222) = HCF(852,315) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 354 > 3, we apply the division lemma to 354 and 3, to get
354 = 3 x 118 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 354 is 3
Notice that 3 = HCF(354,3) .
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 852, 315, 354?
Answer: HCF of 852, 315, 354 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 852, 315, 354 using Euclid's Algorithm?
Answer: For arbitrary numbers 852, 315, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.