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 651, 888, 470 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 651, 888, 470 is 1 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 651, 888, 470 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 651, 888, 470 is 1.
HCF(651, 888, 470) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 651, 888, 470 is 1.
Step 1: Since 888 > 651, we apply the division lemma to 888 and 651, to get
888 = 651 x 1 + 237
Step 2: Since the reminder 651 ≠ 0, we apply division lemma to 237 and 651, to get
651 = 237 x 2 + 177
Step 3: We consider the new divisor 237 and the new remainder 177, and apply the division lemma to get
237 = 177 x 1 + 60
We consider the new divisor 177 and the new remainder 60,and apply the division lemma to get
177 = 60 x 2 + 57
We consider the new divisor 60 and the new remainder 57,and apply the division lemma to get
60 = 57 x 1 + 3
We consider the new divisor 57 and the new remainder 3,and apply the division lemma to get
57 = 3 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 651 and 888 is 3
Notice that 3 = HCF(57,3) = HCF(60,57) = HCF(177,60) = HCF(237,177) = HCF(651,237) = HCF(888,651) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 470 > 3, we apply the division lemma to 470 and 3, to get
470 = 3 x 156 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 470 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(470,3) .
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 651, 888, 470?
Answer: HCF of 651, 888, 470 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 651, 888, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 651, 888, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.