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 264, 43407 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 264, 43407 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 264, 43407 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 264, 43407 is 3.
HCF(264, 43407) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 264, 43407 is 3.
Step 1: Since 43407 > 264, we apply the division lemma to 43407 and 264, to get
43407 = 264 x 164 + 111
Step 2: Since the reminder 264 ≠ 0, we apply division lemma to 111 and 264, to get
264 = 111 x 2 + 42
Step 3: We consider the new divisor 111 and the new remainder 42, and apply the division lemma to get
111 = 42 x 2 + 27
We consider the new divisor 42 and the new remainder 27,and apply the division lemma to get
42 = 27 x 1 + 15
We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get
27 = 15 x 1 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 264 and 43407 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(111,42) = HCF(264,111) = HCF(43407,264) .
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 264, 43407?
Answer: HCF of 264, 43407 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 264, 43407 using Euclid's Algorithm?
Answer: For arbitrary numbers 264, 43407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.