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 990, 624, 557 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 624, 557 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 990, 624, 557 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 990, 624, 557 is 1.
HCF(990, 624, 557) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 990, 624, 557 is 1.
Step 1: Since 990 > 624, we apply the division lemma to 990 and 624, to get
990 = 624 x 1 + 366
Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 366 and 624, to get
624 = 366 x 1 + 258
Step 3: We consider the new divisor 366 and the new remainder 258, and apply the division lemma to get
366 = 258 x 1 + 108
We consider the new divisor 258 and the new remainder 108,and apply the division lemma to get
258 = 108 x 2 + 42
We consider the new divisor 108 and the new remainder 42,and apply the division lemma to get
108 = 42 x 2 + 24
We consider the new divisor 42 and the new remainder 24,and apply the division lemma to get
42 = 24 x 1 + 18
We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 990 and 624 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(42,24) = HCF(108,42) = HCF(258,108) = HCF(366,258) = HCF(624,366) = HCF(990,624) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 557 > 6, we apply the division lemma to 557 and 6, to get
557 = 6 x 92 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 557 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(557,6) .
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 990, 624, 557?
Answer: HCF of 990, 624, 557 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 624, 557 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 624, 557 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.