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 624, 2039, 7305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 624, 2039, 7305 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 624, 2039, 7305 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 624, 2039, 7305 is 1.
HCF(624, 2039, 7305) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 624, 2039, 7305 is 1.
Step 1: Since 2039 > 624, we apply the division lemma to 2039 and 624, to get
2039 = 624 x 3 + 167
Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 167 and 624, to get
624 = 167 x 3 + 123
Step 3: We consider the new divisor 167 and the new remainder 123, and apply the division lemma to get
167 = 123 x 1 + 44
We consider the new divisor 123 and the new remainder 44,and apply the division lemma to get
123 = 44 x 2 + 35
We consider the new divisor 44 and the new remainder 35,and apply the division lemma to get
44 = 35 x 1 + 9
We consider the new divisor 35 and the new remainder 9,and apply the division lemma to get
35 = 9 x 3 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 624 and 2039 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(35,9) = HCF(44,35) = HCF(123,44) = HCF(167,123) = HCF(624,167) = HCF(2039,624) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7305 > 1, we apply the division lemma to 7305 and 1, to get
7305 = 1 x 7305 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7305 is 1
Notice that 1 = HCF(7305,1) .
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 624, 2039, 7305?
Answer: HCF of 624, 2039, 7305 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 624, 2039, 7305 using Euclid's Algorithm?
Answer: For arbitrary numbers 624, 2039, 7305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.