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 715, 988, 676 i.e. 13 the largest integer that leaves a remainder zero for all numbers.
HCF of 715, 988, 676 is 13 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 715, 988, 676 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 715, 988, 676 is 13.
HCF(715, 988, 676) = 13
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 715, 988, 676 is 13.
Step 1: Since 988 > 715, we apply the division lemma to 988 and 715, to get
988 = 715 x 1 + 273
Step 2: Since the reminder 715 ≠ 0, we apply division lemma to 273 and 715, to get
715 = 273 x 2 + 169
Step 3: We consider the new divisor 273 and the new remainder 169, and apply the division lemma to get
273 = 169 x 1 + 104
We consider the new divisor 169 and the new remainder 104,and apply the division lemma to get
169 = 104 x 1 + 65
We consider the new divisor 104 and the new remainder 65,and apply the division lemma to get
104 = 65 x 1 + 39
We consider the new divisor 65 and the new remainder 39,and apply the division lemma to get
65 = 39 x 1 + 26
We consider the new divisor 39 and the new remainder 26,and apply the division lemma to get
39 = 26 x 1 + 13
We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get
26 = 13 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 715 and 988 is 13
Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(65,39) = HCF(104,65) = HCF(169,104) = HCF(273,169) = HCF(715,273) = HCF(988,715) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 676 > 13, we apply the division lemma to 676 and 13, to get
676 = 13 x 52 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 13 and 676 is 13
Notice that 13 = HCF(676,13) .
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 715, 988, 676?
Answer: HCF of 715, 988, 676 is 13 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 715, 988, 676 using Euclid's Algorithm?
Answer: For arbitrary numbers 715, 988, 676 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.