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 527, 310 i.e. 31 the largest integer that leaves a remainder zero for all numbers.
HCF of 527, 310 is 31 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 527, 310 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 527, 310 is 31.
HCF(527, 310) = 31
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 527, 310 is 31.
Step 1: Since 527 > 310, we apply the division lemma to 527 and 310, to get
527 = 310 x 1 + 217
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 217 and 310, to get
310 = 217 x 1 + 93
Step 3: We consider the new divisor 217 and the new remainder 93, and apply the division lemma to get
217 = 93 x 2 + 31
We consider the new divisor 93 and the new remainder 31, and apply the division lemma to get
93 = 31 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 527 and 310 is 31
Notice that 31 = HCF(93,31) = HCF(217,93) = HCF(310,217) = HCF(527,310) .
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 527, 310?
Answer: HCF of 527, 310 is 31 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 527, 310 using Euclid's Algorithm?
Answer: For arbitrary numbers 527, 310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.