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 378, 255, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 255, 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 378, 255, 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 378, 255, 407 is 1.
HCF(378, 255, 407) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 255, 407 is 1.
Step 1: Since 378 > 255, we apply the division lemma to 378 and 255, to get
378 = 255 x 1 + 123
Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 123 and 255, to get
255 = 123 x 2 + 9
Step 3: We consider the new divisor 123 and the new remainder 9, and apply the division lemma to get
123 = 9 x 13 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 378 and 255 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(123,9) = HCF(255,123) = HCF(378,255) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 407 > 3, we apply the division lemma to 407 and 3, to get
407 = 3 x 135 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 407 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(407,3) .
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 378, 255, 407?
Answer: HCF of 378, 255, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 255, 407 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 255, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.