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 5362, 6932, 60900 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5362, 6932, 60900 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 5362, 6932, 60900 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 5362, 6932, 60900 is 2.
HCF(5362, 6932, 60900) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5362, 6932, 60900 is 2.
Step 1: Since 6932 > 5362, we apply the division lemma to 6932 and 5362, to get
6932 = 5362 x 1 + 1570
Step 2: Since the reminder 5362 ≠ 0, we apply division lemma to 1570 and 5362, to get
5362 = 1570 x 3 + 652
Step 3: We consider the new divisor 1570 and the new remainder 652, and apply the division lemma to get
1570 = 652 x 2 + 266
We consider the new divisor 652 and the new remainder 266,and apply the division lemma to get
652 = 266 x 2 + 120
We consider the new divisor 266 and the new remainder 120,and apply the division lemma to get
266 = 120 x 2 + 26
We consider the new divisor 120 and the new remainder 26,and apply the division lemma to get
120 = 26 x 4 + 16
We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get
26 = 16 x 1 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 5362 and 6932 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(120,26) = HCF(266,120) = HCF(652,266) = HCF(1570,652) = HCF(5362,1570) = HCF(6932,5362) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60900 > 2, we apply the division lemma to 60900 and 2, to get
60900 = 2 x 30450 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 60900 is 2
Notice that 2 = HCF(60900,2) .
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 5362, 6932, 60900?
Answer: HCF of 5362, 6932, 60900 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5362, 6932, 60900 using Euclid's Algorithm?
Answer: For arbitrary numbers 5362, 6932, 60900 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.