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 520, 760, 707 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 520, 760, 707 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 520, 760, 707 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 520, 760, 707 is 1.
HCF(520, 760, 707) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 520, 760, 707 is 1.
Step 1: Since 760 > 520, we apply the division lemma to 760 and 520, to get
760 = 520 x 1 + 240
Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 240 and 520, to get
520 = 240 x 2 + 40
Step 3: We consider the new divisor 240 and the new remainder 40, and apply the division lemma to get
240 = 40 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 520 and 760 is 40
Notice that 40 = HCF(240,40) = HCF(520,240) = HCF(760,520) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 707 > 40, we apply the division lemma to 707 and 40, to get
707 = 40 x 17 + 27
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 27 and 40, to get
40 = 27 x 1 + 13
Step 3: We consider the new divisor 27 and the new remainder 13, and apply the division lemma to get
27 = 13 x 2 + 1
We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 40 and 707 is 1
Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(40,27) = HCF(707,40) .
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 520, 760, 707?
Answer: HCF of 520, 760, 707 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 520, 760, 707 using Euclid's Algorithm?
Answer: For arbitrary numbers 520, 760, 707 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.