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 407, 704, 33 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 407, 704, 33 is 11 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 407, 704, 33 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 407, 704, 33 is 11.
HCF(407, 704, 33) = 11
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 407, 704, 33 is 11.
Step 1: Since 704 > 407, we apply the division lemma to 704 and 407, to get
704 = 407 x 1 + 297
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 297 and 407, to get
407 = 297 x 1 + 110
Step 3: We consider the new divisor 297 and the new remainder 110, and apply the division lemma to get
297 = 110 x 2 + 77
We consider the new divisor 110 and the new remainder 77,and apply the division lemma to get
110 = 77 x 1 + 33
We consider the new divisor 77 and the new remainder 33,and apply the division lemma to get
77 = 33 x 2 + 11
We consider the new divisor 33 and the new remainder 11,and apply the division lemma to get
33 = 11 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 407 and 704 is 11
Notice that 11 = HCF(33,11) = HCF(77,33) = HCF(110,77) = HCF(297,110) = HCF(407,297) = HCF(704,407) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 33 > 11, we apply the division lemma to 33 and 11, to get
33 = 11 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 11 and 33 is 11
Notice that 11 = HCF(33,11) .
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 407, 704, 33?
Answer: HCF of 407, 704, 33 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 407, 704, 33 using Euclid's Algorithm?
Answer: For arbitrary numbers 407, 704, 33 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.