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, 884, 661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 624, 884, 661 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, 884, 661 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, 884, 661 is 1.
HCF(624, 884, 661) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 624, 884, 661 is 1.
Step 1: Since 884 > 624, we apply the division lemma to 884 and 624, to get
884 = 624 x 1 + 260
Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 260 and 624, to get
624 = 260 x 2 + 104
Step 3: We consider the new divisor 260 and the new remainder 104, and apply the division lemma to get
260 = 104 x 2 + 52
We consider the new divisor 104 and the new remainder 52, and apply the division lemma to get
104 = 52 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 624 and 884 is 52
Notice that 52 = HCF(104,52) = HCF(260,104) = HCF(624,260) = HCF(884,624) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 661 > 52, we apply the division lemma to 661 and 52, to get
661 = 52 x 12 + 37
Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 37 and 52, to get
52 = 37 x 1 + 15
Step 3: We consider the new divisor 37 and the new remainder 15, and apply the division lemma to get
37 = 15 x 2 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 52 and 661 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(37,15) = HCF(52,37) = HCF(661,52) .
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, 884, 661?
Answer: HCF of 624, 884, 661 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 624, 884, 661 using Euclid's Algorithm?
Answer: For arbitrary numbers 624, 884, 661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.