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 457, 694, 455 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 457, 694, 455 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 457, 694, 455 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 457, 694, 455 is 1.
HCF(457, 694, 455) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 457, 694, 455 is 1.
Step 1: Since 694 > 457, we apply the division lemma to 694 and 457, to get
694 = 457 x 1 + 237
Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 237 and 457, to get
457 = 237 x 1 + 220
Step 3: We consider the new divisor 237 and the new remainder 220, and apply the division lemma to get
237 = 220 x 1 + 17
We consider the new divisor 220 and the new remainder 17,and apply the division lemma to get
220 = 17 x 12 + 16
We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get
17 = 16 x 1 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 694 is 1
Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(220,17) = HCF(237,220) = HCF(457,237) = HCF(694,457) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 455 > 1, we apply the division lemma to 455 and 1, to get
455 = 1 x 455 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 455 is 1
Notice that 1 = HCF(455,1) .
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 457, 694, 455?
Answer: HCF of 457, 694, 455 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 457, 694, 455 using Euclid's Algorithm?
Answer: For arbitrary numbers 457, 694, 455 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.