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, 385, 360 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 715, 385, 360 is 5 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, 385, 360 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, 385, 360 is 5.
HCF(715, 385, 360) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 715, 385, 360 is 5.
Step 1: Since 715 > 385, we apply the division lemma to 715 and 385, to get
715 = 385 x 1 + 330
Step 2: Since the reminder 385 ≠ 0, we apply division lemma to 330 and 385, to get
385 = 330 x 1 + 55
Step 3: We consider the new divisor 330 and the new remainder 55, and apply the division lemma to get
330 = 55 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 55, the HCF of 715 and 385 is 55
Notice that 55 = HCF(330,55) = HCF(385,330) = HCF(715,385) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 360 > 55, we apply the division lemma to 360 and 55, to get
360 = 55 x 6 + 30
Step 2: Since the reminder 55 ≠ 0, we apply division lemma to 30 and 55, to get
55 = 30 x 1 + 25
Step 3: We consider the new divisor 30 and the new remainder 25, and apply the division lemma to get
30 = 25 x 1 + 5
We consider the new divisor 25 and the new remainder 5, and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 55 and 360 is 5
Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(55,30) = HCF(360,55) .
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, 385, 360?
Answer: HCF of 715, 385, 360 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 715, 385, 360 using Euclid's Algorithm?
Answer: For arbitrary numbers 715, 385, 360 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.