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 513, 665, 970 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 665, 970 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 513, 665, 970 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 513, 665, 970 is 1.
HCF(513, 665, 970) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 513, 665, 970 is 1.
Step 1: Since 665 > 513, we apply the division lemma to 665 and 513, to get
665 = 513 x 1 + 152
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 152 and 513, to get
513 = 152 x 3 + 57
Step 3: We consider the new divisor 152 and the new remainder 57, and apply the division lemma to get
152 = 57 x 2 + 38
We consider the new divisor 57 and the new remainder 38,and apply the division lemma to get
57 = 38 x 1 + 19
We consider the new divisor 38 and the new remainder 19,and apply the division lemma to get
38 = 19 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 513 and 665 is 19
Notice that 19 = HCF(38,19) = HCF(57,38) = HCF(152,57) = HCF(513,152) = HCF(665,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 970 > 19, we apply the division lemma to 970 and 19, to get
970 = 19 x 51 + 1
Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 1 and 19, to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 19 and 970 is 1
Notice that 1 = HCF(19,1) = HCF(970,19) .
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 513, 665, 970?
Answer: HCF of 513, 665, 970 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 665, 970 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 665, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.