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 658, 2572, 1265 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 2572, 1265 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 658, 2572, 1265 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 658, 2572, 1265 is 1.
HCF(658, 2572, 1265) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 658, 2572, 1265 is 1.
Step 1: Since 2572 > 658, we apply the division lemma to 2572 and 658, to get
2572 = 658 x 3 + 598
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 598 and 658, to get
658 = 598 x 1 + 60
Step 3: We consider the new divisor 598 and the new remainder 60, and apply the division lemma to get
598 = 60 x 9 + 58
We consider the new divisor 60 and the new remainder 58,and apply the division lemma to get
60 = 58 x 1 + 2
We consider the new divisor 58 and the new remainder 2,and apply the division lemma to get
58 = 2 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 658 and 2572 is 2
Notice that 2 = HCF(58,2) = HCF(60,58) = HCF(598,60) = HCF(658,598) = HCF(2572,658) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1265 > 2, we apply the division lemma to 1265 and 2, to get
1265 = 2 x 632 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 1265 is 1
Notice that 1 = HCF(2,1) = HCF(1265,2) .
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 658, 2572, 1265?
Answer: HCF of 658, 2572, 1265 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 2572, 1265 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 2572, 1265 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.