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 688, 976 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 976 is 16 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 688, 976 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 688, 976 is 16.
HCF(688, 976) = 16
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 976 is 16.
Step 1: Since 976 > 688, we apply the division lemma to 976 and 688, to get
976 = 688 x 1 + 288
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 288 and 688, to get
688 = 288 x 2 + 112
Step 3: We consider the new divisor 288 and the new remainder 112, and apply the division lemma to get
288 = 112 x 2 + 64
We consider the new divisor 112 and the new remainder 64,and apply the division lemma to get
112 = 64 x 1 + 48
We consider the new divisor 64 and the new remainder 48,and apply the division lemma to get
64 = 48 x 1 + 16
We consider the new divisor 48 and the new remainder 16,and apply the division lemma to get
48 = 16 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 688 and 976 is 16
Notice that 16 = HCF(48,16) = HCF(64,48) = HCF(112,64) = HCF(288,112) = HCF(688,288) = HCF(976,688) .
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 688, 976?
Answer: HCF of 688, 976 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 976 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 976 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.