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 310, 534 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 534 is 2 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 310, 534 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 310, 534 is 2.
HCF(310, 534) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 534 is 2.
Step 1: Since 534 > 310, we apply the division lemma to 534 and 310, to get
534 = 310 x 1 + 224
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 224 and 310, to get
310 = 224 x 1 + 86
Step 3: We consider the new divisor 224 and the new remainder 86, and apply the division lemma to get
224 = 86 x 2 + 52
We consider the new divisor 86 and the new remainder 52,and apply the division lemma to get
86 = 52 x 1 + 34
We consider the new divisor 52 and the new remainder 34,and apply the division lemma to get
52 = 34 x 1 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 310 and 534 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(52,34) = HCF(86,52) = HCF(224,86) = HCF(310,224) = HCF(534,310) .
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 310, 534?
Answer: HCF of 310, 534 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 534 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 534 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.