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 508, 7546 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 508, 7546 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 508, 7546 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 508, 7546 is 2.
HCF(508, 7546) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 508, 7546 is 2.
Step 1: Since 7546 > 508, we apply the division lemma to 7546 and 508, to get
7546 = 508 x 14 + 434
Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 434 and 508, to get
508 = 434 x 1 + 74
Step 3: We consider the new divisor 434 and the new remainder 74, and apply the division lemma to get
434 = 74 x 5 + 64
We consider the new divisor 74 and the new remainder 64,and apply the division lemma to get
74 = 64 x 1 + 10
We consider the new divisor 64 and the new remainder 10,and apply the division lemma to get
64 = 10 x 6 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 508 and 7546 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(64,10) = HCF(74,64) = HCF(434,74) = HCF(508,434) = HCF(7546,508) .
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 508, 7546?
Answer: HCF of 508, 7546 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 508, 7546 using Euclid's Algorithm?
Answer: For arbitrary numbers 508, 7546 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.