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 507, 455, 742 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 507, 455, 742 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 507, 455, 742 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 507, 455, 742 is 1.
HCF(507, 455, 742) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 507, 455, 742 is 1.
Step 1: Since 507 > 455, we apply the division lemma to 507 and 455, to get
507 = 455 x 1 + 52
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 52 and 455, to get
455 = 52 x 8 + 39
Step 3: We consider the new divisor 52 and the new remainder 39, and apply the division lemma to get
52 = 39 x 1 + 13
We consider the new divisor 39 and the new remainder 13, and apply the division lemma to get
39 = 13 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 507 and 455 is 13
Notice that 13 = HCF(39,13) = HCF(52,39) = HCF(455,52) = HCF(507,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 742 > 13, we apply the division lemma to 742 and 13, to get
742 = 13 x 57 + 1
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 1 and 13, to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 742 is 1
Notice that 1 = HCF(13,1) = HCF(742,13) .
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 507, 455, 742?
Answer: HCF of 507, 455, 742 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 507, 455, 742 using Euclid's Algorithm?
Answer: For arbitrary numbers 507, 455, 742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.