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 800, 222, 32 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 800, 222, 32 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 800, 222, 32 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 800, 222, 32 is 2.
HCF(800, 222, 32) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 800, 222, 32 is 2.
Step 1: Since 800 > 222, we apply the division lemma to 800 and 222, to get
800 = 222 x 3 + 134
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 134 and 222, to get
222 = 134 x 1 + 88
Step 3: We consider the new divisor 134 and the new remainder 88, and apply the division lemma to get
134 = 88 x 1 + 46
We consider the new divisor 88 and the new remainder 46,and apply the division lemma to get
88 = 46 x 1 + 42
We consider the new divisor 46 and the new remainder 42,and apply the division lemma to get
46 = 42 x 1 + 4
We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get
42 = 4 x 10 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 800 and 222 is 2
Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(46,42) = HCF(88,46) = HCF(134,88) = HCF(222,134) = HCF(800,222) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 2, we apply the division lemma to 32 and 2, to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 32 is 2
Notice that 2 = HCF(32,2) .
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 800, 222, 32?
Answer: HCF of 800, 222, 32 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 800, 222, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 800, 222, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.