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, 288, 992 i.e. 32 the largest integer that leaves a remainder zero for all numbers.
HCF of 800, 288, 992 is 32 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, 288, 992 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, 288, 992 is 32.
HCF(800, 288, 992) = 32
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 800, 288, 992 is 32.
Step 1: Since 800 > 288, we apply the division lemma to 800 and 288, to get
800 = 288 x 2 + 224
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 224 and 288, to get
288 = 224 x 1 + 64
Step 3: We consider the new divisor 224 and the new remainder 64, and apply the division lemma to get
224 = 64 x 3 + 32
We consider the new divisor 64 and the new remainder 32, and apply the division lemma to get
64 = 32 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 800 and 288 is 32
Notice that 32 = HCF(64,32) = HCF(224,64) = HCF(288,224) = HCF(800,288) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 992 > 32, we apply the division lemma to 992 and 32, to get
992 = 32 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 32 and 992 is 32
Notice that 32 = HCF(992,32) .
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, 288, 992?
Answer: HCF of 800, 288, 992 is 32 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 800, 288, 992 using Euclid's Algorithm?
Answer: For arbitrary numbers 800, 288, 992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.