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 450, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 691 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 450, 691 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 450, 691 is 1.
HCF(450, 691) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 450, 691 is 1.
Step 1: Since 691 > 450, we apply the division lemma to 691 and 450, to get
691 = 450 x 1 + 241
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 241 and 450, to get
450 = 241 x 1 + 209
Step 3: We consider the new divisor 241 and the new remainder 209, and apply the division lemma to get
241 = 209 x 1 + 32
We consider the new divisor 209 and the new remainder 32,and apply the division lemma to get
209 = 32 x 6 + 17
We consider the new divisor 32 and the new remainder 17,and apply the division lemma to get
32 = 17 x 1 + 15
We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get
17 = 15 x 1 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 1
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 450 and 691 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(32,17) = HCF(209,32) = HCF(241,209) = HCF(450,241) = HCF(691,450) .
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 450, 691?
Answer: HCF of 450, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 691 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.