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 575, 998, 715 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 575, 998, 715 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 575, 998, 715 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 575, 998, 715 is 1.
HCF(575, 998, 715) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 575, 998, 715 is 1.
Step 1: Since 998 > 575, we apply the division lemma to 998 and 575, to get
998 = 575 x 1 + 423
Step 2: Since the reminder 575 ≠ 0, we apply division lemma to 423 and 575, to get
575 = 423 x 1 + 152
Step 3: We consider the new divisor 423 and the new remainder 152, and apply the division lemma to get
423 = 152 x 2 + 119
We consider the new divisor 152 and the new remainder 119,and apply the division lemma to get
152 = 119 x 1 + 33
We consider the new divisor 119 and the new remainder 33,and apply the division lemma to get
119 = 33 x 3 + 20
We consider the new divisor 33 and the new remainder 20,and apply the division lemma to get
33 = 20 x 1 + 13
We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get
20 = 13 x 1 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 575 and 998 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(33,20) = HCF(119,33) = HCF(152,119) = HCF(423,152) = HCF(575,423) = HCF(998,575) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 715 > 1, we apply the division lemma to 715 and 1, to get
715 = 1 x 715 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 715 is 1
Notice that 1 = HCF(715,1) .
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 575, 998, 715?
Answer: HCF of 575, 998, 715 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 575, 998, 715 using Euclid's Algorithm?
Answer: For arbitrary numbers 575, 998, 715 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.