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 32, 42, 45, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 32, 42, 45, 407 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 32, 42, 45, 407 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 32, 42, 45, 407 is 1.
HCF(32, 42, 45, 407) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 32, 42, 45, 407 is 1.
Step 1: Since 42 > 32, we apply the division lemma to 42 and 32, to get
42 = 32 x 1 + 10
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 10 and 32, to get
32 = 10 x 3 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 32 and 42 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 2, we apply the division lemma to 45 and 2, to get
45 = 2 x 22 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 45 is 1
Notice that 1 = HCF(2,1) = HCF(45,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 407 > 1, we apply the division lemma to 407 and 1, to get
407 = 1 x 407 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 407 is 1
Notice that 1 = HCF(407,1) .
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 32, 42, 45, 407?
Answer: HCF of 32, 42, 45, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 32, 42, 45, 407 using Euclid's Algorithm?
Answer: For arbitrary numbers 32, 42, 45, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.