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 315, 826 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 315, 826 is 7 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 315, 826 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 315, 826 is 7.
HCF(315, 826) = 7
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 315, 826 is 7.
Step 1: Since 826 > 315, we apply the division lemma to 826 and 315, to get
826 = 315 x 2 + 196
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 196 and 315, to get
315 = 196 x 1 + 119
Step 3: We consider the new divisor 196 and the new remainder 119, and apply the division lemma to get
196 = 119 x 1 + 77
We consider the new divisor 119 and the new remainder 77,and apply the division lemma to get
119 = 77 x 1 + 42
We consider the new divisor 77 and the new remainder 42,and apply the division lemma to get
77 = 42 x 1 + 35
We consider the new divisor 42 and the new remainder 35,and apply the division lemma to get
42 = 35 x 1 + 7
We consider the new divisor 35 and the new remainder 7,and apply the division lemma to get
35 = 7 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 315 and 826 is 7
Notice that 7 = HCF(35,7) = HCF(42,35) = HCF(77,42) = HCF(119,77) = HCF(196,119) = HCF(315,196) = HCF(826,315) .
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 315, 826?
Answer: HCF of 315, 826 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 315, 826 using Euclid's Algorithm?
Answer: For arbitrary numbers 315, 826 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.