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 704, 984 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 984 is 8 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 704, 984 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 704, 984 is 8.
HCF(704, 984) = 8
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 704, 984 is 8.
Step 1: Since 984 > 704, we apply the division lemma to 984 and 704, to get
984 = 704 x 1 + 280
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 280 and 704, to get
704 = 280 x 2 + 144
Step 3: We consider the new divisor 280 and the new remainder 144, and apply the division lemma to get
280 = 144 x 1 + 136
We consider the new divisor 144 and the new remainder 136,and apply the division lemma to get
144 = 136 x 1 + 8
We consider the new divisor 136 and the new remainder 8,and apply the division lemma to get
136 = 8 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 704 and 984 is 8
Notice that 8 = HCF(136,8) = HCF(144,136) = HCF(280,144) = HCF(704,280) = HCF(984,704) .
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 704, 984?
Answer: HCF of 704, 984 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 984 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.